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Paul D, Komarova NL. Multi-scale network targeting: A holistic systems-biology approach to cancer treatment. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2021; 165:72-79. [PMID: 34428429 DOI: 10.1016/j.pbiomolbio.2021.08.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Revised: 08/05/2021] [Accepted: 08/10/2021] [Indexed: 11/15/2022]
Abstract
The vulnerabilities of cancer at the cellular and, recently, with the introduction of immunotherapy, at the tissue level, have been exploited with variable success. Evaluating the cancer system vulnerabilities at the organismic level through analysis of network topology and network dynamics can potentially predict novel anti-cancer drug targets directed at the macroscopic cancer networks. Theoretical work analyzing the properties and the vulnerabilities of the multi-scale network of cancer needs to go hand-in-hand with experimental research that uncovers the biological nature of the relevant networks and reveals new targetable vulnerabilities. It is our hope that attacking cancer on different spatial scales, in a concerted integrated approach, may present opportunities for novel ways to prevent treatment resistance.
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Affiliation(s)
- Doru Paul
- Medical Oncology, Weill Cornell Medicine, 1305 York Avenue 12th Floor, New York, NY, 10021, USA.
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA.
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2
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Dawson J, Lee PS, van Rienen U, Appali R. A General Theoretical Framework to Study the Influence of Electrical Fields on Mesenchymal Stem Cells. Front Bioeng Biotechnol 2020; 8:557447. [PMID: 33195123 PMCID: PMC7606877 DOI: 10.3389/fbioe.2020.557447] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 09/08/2020] [Indexed: 12/14/2022] Open
Abstract
Mesenchymal stem cell dynamics involve cell proliferation and cell differentiation into cells of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically active implants influence these dynamics for the regeneration of the cells in damaged tissues. How applied electric field influences processes of individual stem cells is a problem mostly unaddressed. The mathematical approaches to study stem cell dynamics have focused on the stem cell population as a whole, without resolving individual cells and intracellular processes. In this paper, we present a theoretical framework to describe the dynamics of a population of stem cells, taking into account the processes of the individual cells. We study the influence of the applied electric field on the cellular processes. We test our mean-field theory with the experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that a simple model can quantitatively describe the experimentally observed time-course behavior of the total number of cells and the total alkaline phosphate activity in a population of mesenchymal stem cells. Our results show that the stem cell differentiation rate is dependent on the applied electrical field, confirming published experimental findings. Moreover, our analysis supports the cell density-dependent proliferation rate. Since the experimental results are averaged over many cells, our theoretical framework presents a robust and sensitive method for determining the effect of applied electric fields at the scale of the individual cell. These results indicate that the electric field stimulation may be effective in promoting bone regeneration by accelerating osteogenic differentiation.
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Affiliation(s)
- Jonathan Dawson
- Department of Computer Science and Electrical Engineering, Institute of General Electrical Engineering, University of Rostock, Rostock, Germany
| | - Poh Soo Lee
- Max Bergmann Center for Biomaterials, Institute for Materials Science, Technical University of Dresden, Dresden, Germany
| | - Ursula van Rienen
- Department of Computer Science and Electrical Engineering, Institute of General Electrical Engineering, University of Rostock, Rostock, Germany.,Department of Ageing of Individuals and Society, Interdisciplinary Faculty, University of Rostock, Rostock, Germany.,Department of Life, Light and Matter, Interdisciplinary Faculty, University of Rostock, Rostock, Germany
| | - Revathi Appali
- Department of Computer Science and Electrical Engineering, Institute of General Electrical Engineering, University of Rostock, Rostock, Germany.,Department of Ageing of Individuals and Society, Interdisciplinary Faculty, University of Rostock, Rostock, Germany
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Xu S, Kim S, Chen ISY, Chou T. Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque. PLoS Comput Biol 2018; 14:e1006489. [PMID: 30335762 PMCID: PMC6218102 DOI: 10.1371/journal.pcbi.1006489] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Revised: 11/05/2018] [Accepted: 09/05/2018] [Indexed: 01/13/2023] Open
Abstract
In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or “clones.” Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go “extinct” but “resurrect” themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals’ blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions. Hematopoiesis of virally tagged cells in rhesus macaques is analyzed in the context of a mechanistic and statistical model. We find that the clone size distribution and the temporal variability in the abundance of each clone (viral tag) in peripheral blood are consistent with (i) stochastic HSC self-renewal during bone marrow repair, (ii) clonal aging that restricts the number of generations of progenitor cells, and (iii) infrequent and small-size samples. By fitting data, we infer two key parameters that control the level of fluctuations of clone sizes in our model: the total HSC differentiation rate and the maximum proliferation capacity of progenitor cells. Our analysis provides insight into the mechanisms of hematopoiesis and a framework to guide future multiclone barcoding/lineage tracking measurements.
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Affiliation(s)
- Song Xu
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, California, United States of America
| | - Sanggu Kim
- Department of Veterinary Biosciences, The Ohio State University, Columbus, Ohio, United States of America
| | - Irvin S. Y. Chen
- UCLA AIDS Institute and Department of Microbiology, Immunology, and Molecular Genetics, University of California, Los Angeles, Los Angeles, California, United States of America
| | - Tom Chou
- Center for Biomedical Informatics Research, Department of Medicine, Stanford University, Stanford, California, United States of America
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California, United States of America
- * E-mail:
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Yang J, Axelrod DE, Komarova NL. Determining the control networks regulating stem cell lineages in colonic crypts. J Theor Biol 2017; 429:190-203. [PMID: 28669884 PMCID: PMC5689466 DOI: 10.1016/j.jtbi.2017.06.033] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Revised: 05/18/2017] [Accepted: 06/25/2017] [Indexed: 12/27/2022]
Abstract
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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Affiliation(s)
- Jienian Yang
- Department of Mathematics, University of California, Irvine, Irvine, CA 92697 USA
| | - David E Axelrod
- Department of Genetics and Cancer Institute of New Jersey, Rutgers University, Piscataway, NJ 08854-8082, USA
| | - Natalia L Komarova
- Department of Ecology and Evolutionary Biology, University of California, Irvine, Irvine, CA 92697, USA.
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Stability of Control Networks in Autonomous Homeostatic Regulation of Stem Cell Lineages. Bull Math Biol 2017; 80:1345-1365. [PMID: 28508298 DOI: 10.1007/s11538-017-0283-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2016] [Accepted: 04/07/2017] [Indexed: 01/02/2023]
Abstract
Design principles of biological networks have been studied extensively in the context of protein-protein interaction networks, metabolic networks, and regulatory (transcriptional) networks. Here we consider regulation networks that occur on larger scales, namely the cell-to-cell signaling networks that connect groups of cells in multicellular organisms. These are the feedback loops that orchestrate the complex dynamics of cell fate decisions and are necessary for the maintenance of homeostasis in stem cell lineages. We focus on "minimal" networks that are those that have the smallest possible numbers of controls. For such minimal networks, the number of controls must be equal to the number of compartments, and the reducibility/irreducibility of the network (whether or not it can be split into smaller independent sub-networks) is defined by a matrix comprised of the cell number increments induced by each of the controlled processes in each of the compartments. Using the formalism of digraphs, we show that in two-compartment lineages, reducible systems must contain two 1-cycles, and irreducible systems one 1-cycle and one 2-cycle; stability follows from the signs of the controls and does not require magnitude restrictions. In three-compartment systems, irreducible digraphs have a tree structure or have one 3-cycle and at least two more shorter cycles, at least one of which is a 1-cycle. With further work and proper biological validation, our results may serve as a first step toward an understanding of ways in which these networks become dysregulated in cancer.
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Ho N, Chua M, Chui CK. Optimization of cell seeding in a 2D bio-scaffold system using computational models. Comput Biol Med 2017; 84:98-113. [PMID: 28359960 DOI: 10.1016/j.compbiomed.2017.03.013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Revised: 03/16/2017] [Accepted: 03/17/2017] [Indexed: 01/24/2023]
Abstract
The cell expansion process is a crucial part of generating cells on a large-scale level in a bioreactor system. Hence, it is important to set operating conditions (e.g. initial cell seeding distribution, culture medium flow rate) to an optimal level. Often, the initial cell seeding distribution factor is neglected and/or overlooked in the design of a bioreactor using conventional seeding distribution methods. This paper proposes a novel seeding distribution method that aims to maximize cell growth and minimize production time/cost. The proposed method utilizes two computational models; the first model represents cell growth patterns whereas the second model determines optimal initial cell seeding positions for adherent cell expansions. Cell growth simulation from the first model demonstrates that the model can be a representation of various cell types with known probabilities. The second model involves a combination of combinatorial optimization, Monte Carlo and concepts of the first model, and is used to design a multi-layer 2D bio-scaffold system that increases cell production efficiency in bioreactor applications. Simulation results have shown that the recommended input configurations obtained from the proposed optimization method are the most optimal configurations. The results have also illustrated the effectiveness of the proposed optimization method. The potential of the proposed seeding distribution method as a useful tool to optimize the cell expansion process in modern bioreactor system applications is highlighted.
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Affiliation(s)
- Nicholas Ho
- Department of Mechanical Engineering, National University of Singapore, Singapore.
| | - Matthew Chua
- Institute of Systems Science, National University of Singapore, Singapore.
| | - Chee-Kong Chui
- Department of Mechanical Engineering, National University of Singapore, Singapore.
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Shahriyari L, Komarova NL, Jilkine A. The role of cell location and spatial gradients in the evolutionary dynamics of colon and intestinal crypts. Biol Direct 2016; 11:42. [PMID: 27549762 PMCID: PMC4994304 DOI: 10.1186/s13062-016-0141-6] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2016] [Accepted: 07/15/2016] [Indexed: 12/22/2022] Open
Abstract
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.
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Affiliation(s)
- Leili Shahriyari
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Ave, Columbus, 43210, USA
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, 340 Rowland Hall, Irvine, 92697, USA.
| | - Alexandra Jilkine
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, 153 Hurley Hall, Notre Dame, 46556, USA.
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Sun Z, Plikus MV, Komarova NL. Near Equilibrium Calculus of Stem Cells in Application to the Airway Epithelium Lineage. PLoS Comput Biol 2016; 12:e1004990. [PMID: 27427948 PMCID: PMC4948767 DOI: 10.1371/journal.pcbi.1004990] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Accepted: 05/18/2016] [Indexed: 01/16/2023] Open
Abstract
Homeostatic maintenance of tissues is orchestrated by well tuned networks of cellular signaling. Such networks regulate, in a stochastic manner, fates of all cells within the respective lineages. Processes such as symmetric and asymmetric divisions, differentiation, de-differentiation, and death have to be controlled in a dynamic fashion, such that the cell population is maintained at a stable equilibrium, has a sufficiently low level of stochastic variation, and is capable of responding efficiently to external damage. Cellular lineages in real tissues may consist of a number of different cell types, connected by hierarchical relationships, albeit not necessarily linear, and engaged in a number of different processes. Here we develop a general mathematical methodology for near equilibrium studies of arbitrarily complex hierarchical cell populations, under regulation by a control network. This methodology allows us to (1) determine stability properties of the network, (2) calculate the stochastic variance, and (3) predict how different control mechanisms affect stability and robustness of the system. We demonstrate the versatility of this tool by using the example of the airway epithelium lineage. Recent research shows that airway epithelium stem cells divide mostly asymmetrically, while the so-called secretory cells divide predominantly symmetrically. It further provides quantitative data on the recovery dynamics of the airway epithelium, which can include secretory cell de-differentiation. Using our new methodology, we demonstrate that while a number of regulatory networks can be compatible with the observed recovery behavior, the observed division patterns of cells are the most optimal from the viewpoint of homeostatic lineage stability and minimizing the variation of the cell population size. This not only explains the observed yet poorly understood features of airway tissue architecture, but also helps to deduce the information on the still largely hypothetical regulatory mechanisms governing tissue turnover, and lends insight into how different control loops influence the stability and variance properties of cell populations. Tissue stability is the basic property of healthy organs, and yet the mechanisms governing the stable, long-term maintenance of cell numbers in tissues are poorly understood. While more and more signaling pathways are being discovered, for the most part it remains unknown how they are being put together by different cell types into complex, nonlinear, hierarchical control networks that, on the one hand, reliably maintain constant cell numbers, and on the other hand, quickly adjust to oversee the robust response to tissue damage. Theoretical approaches can fill the gap by being able to reconstruct the underlying control network, based on the observations about the aspects of cellular dynamics. We argue that while many hypothetical networks may be capable of basic cell lineage maintenance, some are much more efficient from the viewpoint of variance minimization. Thus, we developed a new methodology that can test various control networks for stability, variance, and robustness. In the example of the airway epithelium that we highlight, it turns out that the evolutionary selected, actual architecture coincides with the mathematically optimal solution that minimizes the fluctuations of cell numbers at homeostasis.
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Affiliation(s)
- Zheng Sun
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
| | - Maksim V. Plikus
- Department of Developmental and Cell Biology, Sue and Bill Gross Stem Cell Research Center and Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
| | - Natalia L. Komarova
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
- Department of Ecology and Evolutionary Biology, University of California, Irvine, Irvine, California, United States of America
- * E-mail:
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Yang J, Plikus MV, Komarova NL. The Role of Symmetric Stem Cell Divisions in Tissue Homeostasis. PLoS Comput Biol 2015; 11:e1004629. [PMID: 26700130 PMCID: PMC4689538 DOI: 10.1371/journal.pcbi.1004629] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2015] [Accepted: 10/27/2015] [Indexed: 11/18/2022] Open
Abstract
Successful maintenance of cellular lineages critically depends on the fate decision dynamics of stem cells (SCs) upon division. There are three possible strategies with respect to SC fate decision symmetry: (a) asymmetric mode, when each and every SC division produces one SC and one non-SC progeny; (b) symmetric mode, when 50% of all divisions produce two SCs and another 50%-two non-SC progeny; (c) mixed mode, when both the asymmetric and two types of symmetric SC divisions co-exist and are partitioned so that long-term net balance of the lineage output stays constant. Theoretically, either of these strategies can achieve lineage homeostasis. However, it remains unclear which strategy(s) are more advantageous and under what specific circumstances, and what minimal control mechanisms are required to operate them. Here we used stochastic modeling to analyze and quantify the ability of different types of divisions to maintain long-term lineage homeostasis, in the context of different control networks. Using the example of a two-component lineage, consisting of SCs and one type of non-SC progeny, we show that its tight homeostatic control is not necessarily associated with purely asymmetric divisions. Through stochastic analysis and simulations we show that asymmetric divisions can either stabilize or destabilize the lineage system, depending on the underlying control network. We further apply our computational model to biological observations in the context of a two-component lineage of mouse epidermis, where autonomous lineage control has been proposed and notable regional differences, in terms of symmetric division ratio, have been noted-higher in thickened epidermis of the paw skin as compared to ear and tail skin. By using our model we propose a possible explanation for the regional differences in epidermal lineage control strategies. We demonstrate how symmetric divisions can work to stabilize paw epidermis lineage, which experiences high level of micro-injuries and a lack of hair follicles as a back-up source of SCs.
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Affiliation(s)
- Jienian Yang
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
| | - Maksim V. Plikus
- Department of Developmental and Cell Biology, Sue and Bill Gross Stem Cell Research Center and Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
| | - Natalia L. Komarova
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
- Department of Ecology and Evolutionary Biology, University of California, Irvine, Irvine, California, United States of America
- * E-mail:
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