1
|
Parigini C, Greulich P. Homeostatic regulation of renewing tissue cell populations via crowding control: stability, robustness and quasi-dedifferentiation. J Math Biol 2024; 88:47. [PMID: 38520536 PMCID: PMC10960778 DOI: 10.1007/s00285-024-02057-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 01/18/2024] [Accepted: 01/28/2024] [Indexed: 03/25/2024]
Abstract
To maintain renewing epithelial tissues in a healthy, homeostatic state, cell divisions and differentiation need to be tightly regulated. Mechanisms of homeostatic regulation often rely on crowding feedback control: cells are able to sense the cell density in their environment, via various molecular and mechanosensing pathways, and respond by adjusting division, differentiation, and cell state transitions appropriately. Here, we determine, via a mathematically rigorous framework, which general conditions for the crowding feedback regulation (i) must be minimally met, and (ii) are sufficient, to allow the maintenance of homeostasis in renewing tissues. We show that those conditions naturally allow for a degree of robustness toward disruption of regulation. Furthermore, intrinsic to this feedback regulation is that stem cell identity is established collectively by the cell population, not by individual cells, which implies the possibility of 'quasi-dedifferentiation', in which cells committed to differentiation may reacquire stem cell properties upon depletion of the stem cell pool. These findings can guide future experimental campaigns to identify specific crowding feedback mechanisms.
Collapse
Affiliation(s)
- Cristina Parigini
- School of Mathematical Sciences, University of Southampton, Southampton, UK
- Institute for Life Sciences, University of Southampton, Southampton, UK
- Te Pūnaha Ātea - Space Institute, University of Auckland, Auckland, New Zealand
| | - Philip Greulich
- School of Mathematical Sciences, University of Southampton, Southampton, UK.
- Institute for Life Sciences, University of Southampton, Southampton, UK.
| |
Collapse
|
2
|
Greulich P. Quantitative Modelling in Stem Cell Biology and Beyond: How to Make Best Use of It. Curr Stem Cell Rep 2023; 9:67-76. [PMID: 38145009 PMCID: PMC10739548 DOI: 10.1007/s40778-023-00230-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/17/2023] [Indexed: 12/26/2023]
Abstract
Purpose of Review This article gives a broad overview of quantitative modelling approaches in biology and provides guidance on how to employ them to boost stem cell research, by helping to answer biological questions and to predict the outcome of biological processes. Recent Findings The twenty-first century has seen a steady increase in the proportion of cell biology publications employing mathematical modelling to aid experimental research. However, quantitative modelling is often used as a rather decorative element to confirm experimental findings, an approach which often yields only marginal added value, and is in many cases scientifically questionable. Summary Quantitative modelling can boost biological research in manifold ways, but one has to take some careful considerations before embarking on a modelling campaign, in order to maximise its added value, to avoid pitfalls that may lead to wrong results, and to be aware of its fundamental limitations, imposed by the risks of over-fitting and "universality".
Collapse
Affiliation(s)
- Philip Greulich
- School of Mathematical Sciences, University of Southampton, Southampton, UK
- Institute for Life Sciences, University of Southampton, Southampton, UK
| |
Collapse
|
3
|
Barry-Carroll L, Greulich P, Marshall AR, Riecken K, Fehse B, Askew KE, Li K, Garaschuk O, Menassa DA, Gomez-Nicola D. Microglia colonize the developing brain by clonal expansion of highly proliferative progenitors, following allometric scaling. Cell Rep 2023; 42:112425. [PMID: 37099424 DOI: 10.1016/j.celrep.2023.112425] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Revised: 01/25/2023] [Accepted: 04/06/2023] [Indexed: 04/27/2023] Open
Abstract
Microglia arise from the yolk sac and enter the brain during early embryogenesis. Upon entry, microglia undergo in situ proliferation and eventually colonize the entire brain by the third postnatal week in mice. However, the intricacies of their developmental expansion remain unclear. Here, we characterize the proliferative dynamics of microglia during embryonic and postnatal development using complementary fate-mapping techniques. We demonstrate that the developmental colonization of the brain is facilitated by clonal expansion of highly proliferative microglial progenitors that occupy spatial niches throughout the brain. Moreover, the spatial distribution of microglia switches from a clustered to a random pattern between embryonic and late postnatal development. Interestingly, the developmental increase in microglial numbers follows the proportional growth of the brain in an allometric manner until a mosaic distribution has been established. Overall, our findings offer insight into how the competition for space may drive microglial colonization by clonal expansion during development.
Collapse
Affiliation(s)
- Liam Barry-Carroll
- School of Biological Sciences, University of Southampton, Southampton General Hospital, Southampton, UK
| | - Philip Greulich
- School of Mathematical Sciences, University of Southampton, Southampton, UK; Institute for Life Sciences (IfLS), University of Southampton, Southampton, UK
| | - Abigail R Marshall
- School of Biological Sciences, University of Southampton, Southampton General Hospital, Southampton, UK
| | - Kristoffer Riecken
- Research Department Cell and Gene Therapy, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Boris Fehse
- Research Department Cell and Gene Therapy, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Katharine E Askew
- School of Biological Sciences, University of Southampton, Southampton General Hospital, Southampton, UK
| | - Kaizhen Li
- Department of Neurophysiology, University of Tübingen, Tübingen, Germany
| | - Olga Garaschuk
- Department of Neurophysiology, University of Tübingen, Tübingen, Germany
| | - David A Menassa
- School of Biological Sciences, University of Southampton, Southampton General Hospital, Southampton, UK; The Queen's College, University of Oxford, Oxford, UK
| | - Diego Gomez-Nicola
- School of Biological Sciences, University of Southampton, Southampton General Hospital, Southampton, UK; Institute for Life Sciences (IfLS), University of Southampton, Southampton, UK.
| |
Collapse
|
4
|
Greulich P, MacArthur BD, Parigini C, Sánchez-García RJ. Universal principles of lineage architecture and stem cell identity in renewing tissues. Development 2021; 148:269055. [PMID: 34100065 DOI: 10.1242/dev.194399] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 04/01/2021] [Indexed: 01/20/2023]
Abstract
Adult tissues in multicellular organisms typically contain a variety of stem, progenitor and differentiated cell types arranged in a lineage hierarchy that regulates healthy tissue turnover. Lineage hierarchies in disparate tissues often exhibit common features, yet the general principles regulating their architecture are not known. Here, we provide a formal framework for understanding the relationship between cell molecular 'states' and cell 'types', based on the topology of admissible cell state trajectories. We show that a self-renewing cell type - if defined as suggested by this framework - must reside at the top of any homeostatic renewing lineage hierarchy, and only there. This architecture arises as a natural consequence of homeostasis, and indeed is the only possible way that lineage architectures can be constructed to support homeostasis in renewing tissues. Furthermore, under suitable feedback regulation, for example from the stem cell niche, we show that the property of 'stemness' is entirely determined by the cell environment, in accordance with the notion that stem cell identities are contextual and not determined by hard-wired, cell-intrinsic characteristics. This article has an associated 'The people behind the papers' interview.
Collapse
Affiliation(s)
- Philip Greulich
- Mathematical Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.,Institute for Life Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
| | - Ben D MacArthur
- Mathematical Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.,Institute for Life Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.,Centre for Human Development, Stem Cells and Regeneration, Faculty of Medicine, University of Southampton, Southampton SO17 1BJ, UK.,The Alan Turing Institute, London, NW1 2DB, UK
| | - Cristina Parigini
- Mathematical Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.,Institute for Life Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
| | - Rubén J Sánchez-García
- Mathematical Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.,Institute for Life Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
| |
Collapse
|
5
|
Parigini C, Greulich P. Universality of clonal dynamics poses fundamental limits to identify stem cell self-renewal strategies. eLife 2020; 9:56532. [PMID: 32687057 PMCID: PMC7444910 DOI: 10.7554/elife.56532] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Accepted: 07/03/2020] [Indexed: 12/21/2022] Open
Abstract
How adult stem cells maintain self-renewing tissues is commonly assessed by analysing clonal data from in vivo cell lineage-tracing assays. To identify strategies of stem cell self-renewal requires that different models of stem cell fate choice predict sufficiently different clonal statistics. Here, we show that models of cell fate choice can, in homeostatic tissues, be categorized by exactly two 'universality classes', whereby models of the same class predict, under asymptotic conditions, the same clonal statistics. Those classes relate to generalizations of the canonical asymmetric vs. symmetric stem cell self-renewal strategies and are distinguished by a conservation law. This poses both challenges and opportunities to identify stem cell self-renewal strategies: while under asymptotic conditions, self-renewal models of the same universality class cannot be distinguished by clonal data only, models of different classes can be distinguished by simple means.
Collapse
Affiliation(s)
- Cristina Parigini
- School of Mathematical Science, University of Southampton, Southampton, United Kingdom.,Institute for Life Sciences, University of Southampton, Southampton, United Kingdom
| | - Philip Greulich
- School of Mathematical Science, University of Southampton, Southampton, United Kingdom.,Institute for Life Sciences, University of Southampton, Southampton, United Kingdom
| |
Collapse
|
6
|
Greulich P, MacArthur BD, Parigini C, Sánchez-García RJ. Stability and steady state of complex cooperative systems: a diakoptic approach. R Soc Open Sci 2019; 6:191090. [PMID: 31903203 PMCID: PMC6936286 DOI: 10.1098/rsos.191090] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 11/04/2019] [Indexed: 06/10/2023]
Abstract
Cooperative dynamics are common in ecology and population dynamics. However, their commonly high degree of complexity with a large number of coupled degrees of freedom renders them difficult to analyse. Here, we present a graph-theoretical criterion, via a diakoptic approach (divide-and-conquer) to determine a cooperative system's stability by decomposing the system's dependence graph into its strongly connected components (SCCs). In particular, we show that a linear cooperative system is Lyapunov stable if the SCCs of the associated dependence graph all have non-positive dominant eigenvalues, and if no SCCs which have dominant eigenvalue zero are connected by a path.
Collapse
Affiliation(s)
- Philip Greulich
- School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton SO17 1BJ, UK
| | - Ben D. MacArthur
- School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton SO17 1BJ, UK
- Centre for Human Development, Stem Cells and Regeneration, University of Southampton, Southampton SO17 1BJ, UK
| | - Cristina Parigini
- School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton SO17 1BJ, UK
| | - Rubén J. Sánchez-García
- School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK
- Institute for Life Sciences, University of Southampton, Southampton SO17 1BJ, UK
| |
Collapse
|
7
|
Cholewa-Waclaw J, Shah R, Webb S, Chhatbar K, Ramsahoye B, Pusch O, Yu M, Greulich P, Waclaw B, Bird AP. Quantitative modelling predicts the impact of DNA methylation on RNA polymerase II traffic. Proc Natl Acad Sci U S A 2019; 116:14995-15000. [PMID: 31289233 PMCID: PMC6660794 DOI: 10.1073/pnas.1903549116] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Patterns of gene expression are primarily determined by proteins that locally enhance or repress transcription. While many transcription factors target a restricted number of genes, others appear to modulate transcription levels globally. An example is MeCP2, an abundant methylated-DNA binding protein that is mutated in the neurological disorder Rett syndrome. Despite much research, the molecular mechanism by which MeCP2 regulates gene expression is not fully resolved. Here, we integrate quantitative, multidimensional experimental analysis and mathematical modeling to indicate that MeCP2 is a global transcriptional regulator whose binding to DNA creates "slow sites" in gene bodies. We hypothesize that waves of slowed-down RNA polymerase II formed behind these sites travel backward and indirectly affect initiation, reminiscent of defect-induced shockwaves in nonequilibrium physics transport models. This mechanism differs from conventional gene-regulation mechanisms, which often involve direct modulation of transcription initiation. Our findings point to a genome-wide function of DNA methylation that may account for the reversibility of Rett syndrome in mice. Moreover, our combined theoretical and experimental approach provides a general method for understanding how global gene-expression patterns are choreographed.
Collapse
Affiliation(s)
- Justyna Cholewa-Waclaw
- The Wellcome Centre for Cell Biology, University of Edinburgh, EH9 3BF Edinburgh, United Kingdom
| | - Ruth Shah
- The Wellcome Centre for Cell Biology, University of Edinburgh, EH9 3BF Edinburgh, United Kingdom
| | - Shaun Webb
- The Wellcome Centre for Cell Biology, University of Edinburgh, EH9 3BF Edinburgh, United Kingdom
| | - Kashyap Chhatbar
- The Wellcome Centre for Cell Biology, University of Edinburgh, EH9 3BF Edinburgh, United Kingdom
| | - Bernard Ramsahoye
- Institute of Genetics and Molecular Medicine, University of Edinburgh, Western General Hospital Campus, EH4 2XU Edinburgh, United Kingdom
| | - Oliver Pusch
- Center for Anatomy and Cell Biology, Medical University of Vienna, 1090 Vienna, Austria
| | - Miao Yu
- Ludwig Institute for Cancer Research, San Diego Branch, La Jolla, CA 92093
| | - Philip Greulich
- Mathematical Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom
- Institute for Life Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Bartlomiej Waclaw
- School of Physics and Astronomy, University of Edinburgh, EH9 3FD Edinburgh, United Kingdom
| | - Adrian P Bird
- The Wellcome Centre for Cell Biology, University of Edinburgh, EH9 3BF Edinburgh, United Kingdom;
| |
Collapse
|
8
|
Abstract
Studying cell fate dynamics is complicated by the fact that direct in vivo observation of individual cell fate outcomes is usually not possible and only multicellular data of cell clones can be obtained. In this situation, experimental data alone is not sufficient to validate biological models because the hypotheses and the data cannot be directly compared and thus standard statistical tests cannot be leveraged. On the other hand, mathematical modelling can bridge the scales between a hypothesis and measured data via quantitative predictions from a mathematical model. Here, we describe how to implement the rules behind a hypothesis (cell fate outcomes) one-to-one as a stochastic model, how to evaluate such a rule-based model mathematically via analytical calculation or stochastic simulations of the model's Master equation, and to predict the outcomes of clonal statistics for respective hypotheses. We also illustrate two approaches to compare these predictions directly with the clonal data to assess the models.
Collapse
Affiliation(s)
- Philip Greulich
- Mathematical Sciences, University of Southampton, Southampton, UK.
- Institute for Life Sciences, University of Southampton, Southampton, UK.
| |
Collapse
|
9
|
Abstract
Understanding how antibiotics inhibit bacteria can help to reduce antibiotic use and hence avoid antimicrobial resistance—yet few theoretical models exist for bacterial growth inhibition by a clinically relevant antibiotic treatment regimen. In particular, in the clinic, antibiotic treatment is time-dependent. Here, we use a theoretical model, previously applied to steady-state bacterial growth, to predict the dynamical response of a bacterial cell to a time-dependent dose of ribosome-targeting antibiotic. Our results depend strongly on whether the antibiotic shows reversible transport and/or low-affinity ribosome binding (‘low-affinity antibiotic’) or, in contrast, irreversible transport and/or high affinity ribosome binding (‘high-affinity antibiotic’). For low-affinity antibiotics, our model predicts that growth inhibition depends on the duration of the antibiotic pulse, and can show a transient period of very fast growth following removal of the antibiotic. For high-affinity antibiotics, growth inhibition depends on peak dosage rather than dose duration, and the model predicts a pronounced post-antibiotic effect, due to hysteresis, in which growth can be suppressed for long times after the antibiotic dose has ended. These predictions are experimentally testable and may be of clinical significance.
Collapse
Affiliation(s)
- Philip Greulich
- Mathematical Sciences, University of Southampton, Highfield Campus, SO17 1BJ, United Kingdom. Institute for Life Sciences, University of Southampton, Highfield Campus, SO17 1BJ, United Kingdom
| | | | | | | | | |
Collapse
|
10
|
Frede J, Greulich P, Nagy T, Simons BD, Jones PH. A single dividing cell population with imbalanced fate drives oesophageal tumour growth. Nat Cell Biol 2016; 18:967-78. [PMID: 27548914 PMCID: PMC5870829 DOI: 10.1038/ncb3400] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2016] [Accepted: 07/19/2016] [Indexed: 02/06/2023]
Abstract
Understanding the cellular mechanisms of tumour growth is key for designing rational anticancer treatment. Here we used genetic lineage tracing to quantify cell behaviour during neoplastic transformation in a model of oesophageal carcinogenesis. We found that cell behaviour was convergent across premalignant tumours, which contained a single proliferating cell population. The rate of cell division was not significantly different in the lesions and the surrounding epithelium. However, dividing tumour cells had a uniform, small bias in cell fate so that, on average, slightly more dividing than non-dividing daughter cells were generated at each round of cell division. In invasive cancers induced by Kras(G12D) expression, dividing cell fate became more strongly biased towards producing dividing over non-dividing cells in a subset of clones. These observations argue that agents that restore the balance of cell fate may prove effective in checking tumour growth, whereas those targeting cycling cells may show little selectivity.
Collapse
Affiliation(s)
- Julia Frede
- Wellcome Trust Sanger Institute, Hinxton, CB10 1SA, UK
| | - Philip Greulich
- Cavendish Laboratory, Department of Physics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
- The Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Tennis Court Road, Cambridge CB2 1QN, UK
| | - Tibor Nagy
- Wellcome Trust Sanger Institute, Hinxton, CB10 1SA, UK
| | - Benjamin D Simons
- Cavendish Laboratory, Department of Physics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
- The Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Tennis Court Road, Cambridge CB2 1QN, UK
- Wellcome Trust-Medical Research Council Stem Cell Institute, University of Cambridge, UK
| | - Philip H Jones
- Wellcome Trust Sanger Institute, Hinxton, CB10 1SA, UK
- MRC Cancer Unit, University of Cambridge, Hutchison-MRC Research Centre, Box 197, Cambridge Biomedical Campus, Cambridge, CB2 0XZ, UK
| |
Collapse
|
11
|
Abstract
Bacterial growth environment strongly influences the efficacy of antibiotic treatment, with slow growth often being associated with decreased susceptibility. Yet in many cases, the connection between antibiotic susceptibility and pathogen physiology remains unclear. We show that for ribosome-targeting antibiotics acting on Escherichia coli, a complex interplay exists between physiology and antibiotic action; for some antibiotics within this class, faster growth indeed increases susceptibility, but for other antibiotics, the opposite is true. Remarkably, these observations can be explained by a simple mathematical model that combines drug transport and binding with physiological constraints. Our model reveals that growth-dependent susceptibility is controlled by a single parameter characterizing the ‘reversibility’ of ribosome-targeting antibiotic transport and binding. This parameter provides a spectrum classification of antibiotic growth-dependent efficacy that appears to correspond at its extremes to existing binary classification schemes. In these limits, the model predicts universal, parameter-free limiting forms for growth inhibition curves. The model also leads to non-trivial predictions for the drug susceptibility of a translation mutant strain of E. coli, which we verify experimentally. Drug action and bacterial metabolism are mechanistically complex; nevertheless, this study illustrates how coarse-grained models can be used to integrate pathogen physiology into drug design and treatment strategies.
Collapse
Affiliation(s)
- Philip Greulich
- Cavendish Laboratory, University of CambridgeCambridge, UK
- SUPA, School of Physics and Astronomy, University of EdinburghEdinburgh, UK
| | - Matthew Scott
- Department of Applied Mathematics, University of WaterlooWaterloo, ON, Canada
| | - Martin R Evans
- SUPA, School of Physics and Astronomy, University of EdinburghEdinburgh, UK
| | - Rosalind J Allen
- SUPA, School of Physics and Astronomy, University of EdinburghEdinburgh, UK
- * Corresponding author. Tel: +44 131 6517197; E-mail:
| |
Collapse
|
12
|
Alcolea MP, Greulich P, Wabik A, Frede J, Simons BD, Jones PH. Differentiation imbalance in single oesophageal progenitor cells causes clonal immortalization and field change. Nat Cell Biol 2014; 16:615-22. [PMID: 24814514 PMCID: PMC4085550 DOI: 10.1038/ncb2963] [Citation(s) in RCA: 119] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Accepted: 04/04/2014] [Indexed: 01/18/2023]
Abstract
Multiple cancers may arise from within a clonal region of preneoplastic epithelium, a phenomenon termed 'field change'. However, it is not known how field change develops. Here we investigate this question using lineage tracing to track the behaviour of scattered single oesophageal epithelial progenitor cells expressing a mutation that inhibits the Notch signalling pathway. Notch is frequently subject to inactivating mutation in squamous cancers. Quantitative analysis reveals that cell divisions that produce two differentiated daughters are absent from mutant progenitors. As a result, mutant clones are no longer lost by differentiation and become functionally immortal. Furthermore, mutant cells promote the differentiation of neighbouring wild-type cells, which are then lost from the tissue. These effects lead to clonal expansion, with mutant cells eventually replacing the entire epithelium. Notch inhibition in progenitors carrying p53 stabilizing mutations creates large confluent regions of doubly mutant epithelium. Field change is thus a consequence of imbalanced differentiation in individual progenitor cells.
Collapse
Affiliation(s)
- Maria P. Alcolea
- MRC Cancer Unit, University of Cambridge, Hutchison-MRC Research Centre, Box 197, Cambridge Biomedical Campus, Cambridge, CB2 0XZ, UK
| | - Philip Greulich
- Cavendish Laboratory, Department of Physics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
| | - Agnieszka Wabik
- MRC Cancer Unit, University of Cambridge, Hutchison-MRC Research Centre, Box 197, Cambridge Biomedical Campus, Cambridge, CB2 0XZ, UK
| | - Julia Frede
- MRC Cancer Unit, University of Cambridge, Hutchison-MRC Research Centre, Box 197, Cambridge Biomedical Campus, Cambridge, CB2 0XZ, UK
| | - Benjamin D. Simons
- Cavendish Laboratory, Department of Physics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
- The Wellcome Trust-Cancer Research UK Gurdon Institute, University of Cambridge, Tennis Court Road, Cambridge CB2 1QN, UK
- Wellcome Trust-Medical Research Council Stem Cell Institute, University of Cambridge, UK
| | - Philip H. Jones
- MRC Cancer Unit, University of Cambridge, Hutchison-MRC Research Centre, Box 197, Cambridge Biomedical Campus, Cambridge, CB2 0XZ, UK
| |
Collapse
|
13
|
Greulich P, Waclaw B, Allen RJ. Mutational pathway determines whether drug gradients accelerate evolution of drug-resistant cells. Phys Rev Lett 2012; 109:088101. [PMID: 23002776 DOI: 10.1103/physrevlett.109.088101] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2012] [Indexed: 05/28/2023]
Abstract
Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anticancer drugs. We use a statistical physics model to study the evolution of a population of malignant cells exposed to drug gradients, where drug resistance emerges via a mutational pathway involving multiple mutations. We show that a nonuniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients. These predictions can be verified experimentally, and may help to improve strategies for combating the emergence of resistance.
Collapse
Affiliation(s)
- Philip Greulich
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
| | | | | |
Collapse
|
14
|
Greulich P, Ciandrini L, Allen RJ, Romano MC. Mixed population of competing totally asymmetric simple exclusion processes with a shared reservoir of particles. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 85:011142. [PMID: 22400547 PMCID: PMC3639544 DOI: 10.1103/physreve.85.011142] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Indexed: 05/29/2023]
Abstract
We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths and entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: These relations allow us to show that competition for particles can have nontrivial effects on the phase behavior of individual lattices. For a system with nonidentical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters and could easily be extended beyond the mean-field case.
Collapse
Affiliation(s)
- Philip Greulich
- SUPA, School of Physics & Astronomy, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
| | - Luca Ciandrini
- SUPA, Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - Rosalind J. Allen
- SUPA, School of Physics & Astronomy, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
| | - M. Carmen Romano
- SUPA, Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
- Institute of Medical Sciences, Foresterhill, University of Aberdeen, Aberdeen AB25 2ZD, United Kingdom
| |
Collapse
|
15
|
Greulich P, Santen L. Boundary-induced orientation of dynamic filament networks and vesicle agglomerations. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:060902. [PMID: 22304033 DOI: 10.1103/physreve.84.060902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2011] [Indexed: 05/31/2023]
Abstract
We find a statistical mechanism that can adjust orientations of intracellular filaments to cell geometry in the absence of organizing centers. The effect is based on random and isotropic filament (de-)polymerization dynamics and is independent of filament interactions and explicit regulation. It can be understood by an analogy to electrostatics and appears to be induced by the confining boundaries; for periodic boundary conditions, no orientational bias emerges. Including active transport of particles, the model reproduces experimental observations of vesicle accumulations in transected axons.
Collapse
Affiliation(s)
- Philip Greulich
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
| | | |
Collapse
|
16
|
Greulich P, Santen L. Active transport and cluster formation on 2D networks. Eur Phys J E Soft Matter 2010; 32:191-208. [PMID: 20556462 DOI: 10.1140/epje/i2010-10603-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Accepted: 05/04/2010] [Indexed: 05/29/2023]
Abstract
We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.
Collapse
Affiliation(s)
- P Greulich
- Fachrichtung Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany.
| | | |
Collapse
|
17
|
Greulich P, Schadschneider A. Disordered driven lattice gases with boundary reservoirs and Langmuir kinetics. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:031107. [PMID: 19391902 DOI: 10.1103/physreve.79.031107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2008] [Indexed: 05/27/2023]
Abstract
The asymmetric simple exclusion process with additional Langmuir kinetics, i.e., attachment and detachment in the bulk, is a paradigmatic model for intracellular transport. Here we study this model in the presence of randomly distributed inhomogeneities ("defects"). Using Monte Carlo simulations, we find a multitude of coexisting high- and low-density domains. The results are generic for one-dimensional driven diffusive systems with short-range interactions and can be understood in terms of a local extremal principle for the current profile. This principle is used to determine current profiles and phase diagrams as well as statistical properties of ensembles of defect samples.
Collapse
Affiliation(s)
- Philip Greulich
- Fachrichtung Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany and Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
| | | |
Collapse
|
18
|
Greulich P, Garai A, Nishinari K, Schadschneider A, Chowdhury D. Intracellular transport by single-headed kinesin KIF1A: effects of single-motor mechanochemistry and steric interactions. Phys Rev E Stat Nonlin Soft Matter Phys 2007; 75:041905. [PMID: 17500919 DOI: 10.1103/physreve.75.041905] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2006] [Indexed: 05/15/2023]
Abstract
In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena such as jamming. Recently we reported [Phys. Rev. Lett. 95, 118101 (2005)] a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing an interaction parameter c, to account for an interesting mechanochemical process. We have been able to extract all the parameters of the model, except c, from experimentally measured quantities. In contrast to earlier models of intracellular molecular motor traffic, our model assigns distinct "chemical" (or, conformational) states to each kinesin to account for the hydrolysis of adenosine triphosphate (ATP), the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine, e.g., the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechanochemical process captured by the parameter c.
Collapse
Affiliation(s)
- Philip Greulich
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
| | | | | | | | | |
Collapse
|