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Babajanyan SG, Garushyants SK, Wolf YI, Koonin EV. Microbial diversity and ecological complexity emerging from environmental variation and horizontal gene transfer in a simple mathematical model. BMC Biol 2024; 22:148. [PMID: 38965531 PMCID: PMC11225191 DOI: 10.1186/s12915-024-01937-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Accepted: 06/13/2024] [Indexed: 07/06/2024] Open
Abstract
BACKGROUND Microbiomes are generally characterized by high diversity of coexisting microbial species and strains, and microbiome composition typically remains stable across a broad range of conditions. However, under fixed conditions, microbial ecology conforms with the exclusion principle under which two populations competing for the same resource within the same niche cannot coexist because the less fit population inevitably goes extinct. Therefore, the long-term persistence of microbiome diversity calls for an explanation. RESULTS To explore the conditions for stabilization of microbial diversity, we developed a simple mathematical model consisting of two competing populations that could exchange a single gene allele via horizontal gene transfer (HGT). We found that, although in a fixed environment, with unbiased HGT, the system obeyed the exclusion principle, in an oscillating environment, within large regions of the phase space bounded by the rates of reproduction and HGT, the two populations coexist. Moreover, depending on the parameter combination, all three major types of symbiosis were obtained, namely, pure competition, host-parasite relationship, and mutualism. In each of these regimes, certain parameter combinations provided for synergy, that is, a greater total abundance of both populations compared to the abundance of the winning population in the fixed environment. CONCLUSIONS The results of this modeling study show that basic phenomena that are universal in microbial communities, namely, environmental variation and HGT, provide for stabilization and persistence of microbial diversity, and emergence of ecological complexity.
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Affiliation(s)
- Sanasar G Babajanyan
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, 20894, MD, USA.
| | - Sofya K Garushyants
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, 20894, MD, USA
| | - Yuri I Wolf
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, 20894, MD, USA
| | - Eugene V Koonin
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, 20894, MD, USA.
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Babajanyan SG, Garushyants SK, Wolf YI, Koonin EV. Microbial diversity and ecological complexity emerging from environmental variation and horizontal gene transfer in a simple mathematical model. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.17.576128. [PMID: 38313259 PMCID: PMC10836074 DOI: 10.1101/2024.01.17.576128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2024]
Abstract
Microbiomes are generally characterized by high diversity of coexisting microbial species and strains that remains stable within a broad range of conditions. However, under fixed conditions, microbial ecology conforms with the exclusion principle under which two populations competing for the same resource within the same niche cannot coexist because the less fit population inevitably goes extinct. To explore the conditions for stabilization of microbial diversity, we developed a simple mathematical model consisting of two competing populations that could exchange a single gene allele via horizontal gene transfer (HGT). We found that, although in a fixed environment, with unbiased HGT, the system obeyed the exclusion principle, in an oscillating environment, within large regions of the phase space bounded by the rates of reproduction and HGT, the two populations coexist. Moreover, depending on the parameter combination, all three major types of symbiosis obtained, namely, pure competition, host-parasite relationship and mutualism. In each of these regimes, certain parameter combinations provided for synergy, that is, a greater total abundance of both populations compared to the abundance of the winning population in the fixed environments. These findings show that basic phenomena that are universal in microbial communities, environmental variation and HGT, provide for stabilization of microbial diversity and ecological complexity.
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Affiliation(s)
- Sanasar G. Babajanyan
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA
| | - Sofya K. Garushyants
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA
| | - Yuri I. Wolf
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA
| | - Eugene V. Koonin
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA
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Jiang Y, Wang X, Liu L, Wei M, Zhao J, Zheng Z, Tang S. Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks. PLoS Comput Biol 2023; 19:e1011269. [PMID: 37379330 DOI: 10.1371/journal.pcbi.1011269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 06/13/2023] [Indexed: 06/30/2023] Open
Abstract
Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the 'eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differ in static and dynamic global environments. In particular, we find the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Further, we observe that this cyclic evolution disappears and transforms into an interior stable equilibrium when the global environment is frequency-dependent. Our results provide important insights into how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments.
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Affiliation(s)
- Yishen Jiang
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Xin Wang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Longzhao Liu
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Ming Wei
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Jingwu Zhao
- School of Law, Beihang University, Beijing, China
| | - Zhiming Zheng
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
| | - Shaoting Tang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
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Ionescu F, Zhang J, Wang L. Clinical Applications of Liquid Biopsy in Prostate Cancer: From Screening to Predictive Biomarker. Cancers (Basel) 2022; 14:1728. [PMID: 35406500 PMCID: PMC8996910 DOI: 10.3390/cancers14071728] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Revised: 03/26/2022] [Accepted: 03/27/2022] [Indexed: 01/15/2023] Open
Abstract
Prostate cancer (PC) remains the most common malignancy and the second most common cause of cancer death in men. As a result of highly variable biological behavior and development of resistance to available agents under therapeutic pressure, optimal management is often unclear. Traditional surgical biopsies, even when augmented by genomic studies, may fail to provide adequate guidance for clinical decisions as these can only provide a snapshot of a dynamic process. Additionally, surgical biopsies are cumbersome to perform repeatedly and often involve risk. Liquid biopsies (LB) are defined as the analysis of either corpuscular (circulating tumor cells, extracellular vesicles) or molecular (circulating DNA or RNA) tumor-derived material. LB could more precisely identify clinically relevant alterations that characterize the metastatic potential of tumors, predict response to specific treatments or actively monitor for the emergence of resistance. These tests can potentially be repeated as often as deemed necessary and can detect real-time response to treatment with minimal inconvenience to the patient. In the current review, we consider common clinical scenarios to describe available LB assays in PC as a platform to explore existing evidence for their use in guiding decision making and to discuss current limitations to their adoption in the clinic.
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Affiliation(s)
- Filip Ionescu
- Department of Oncologic Sciences, Morsani College of Medicine, University of South Florida, Tampa, FL 33612, USA;
| | - Jingsong Zhang
- Department of Genitourinary Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612, USA
| | - Liang Wang
- Department of Tumor Biology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612, USA
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Optimizing Adaptive Therapy Based on the Reachability to Tumor Resistant Subpopulation. Cancers (Basel) 2021; 13:cancers13215262. [PMID: 34771426 PMCID: PMC8582524 DOI: 10.3390/cancers13215262] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Revised: 10/14/2021] [Accepted: 10/18/2021] [Indexed: 11/26/2022] Open
Abstract
Simple Summary The intra-competition among tumor subpopulations is a promising target to modify and control the outgrowth of the resistant subpopulation. Adaptive therapy lives up to this principle well, but the gain of tumors with an aggressive resistant subpopulation is not superior to maximum tolerated dose therapy (MTD). How to integrate these two therapies to maximize the outcome? According to the model and system reachability, the ‘restore index’ is proposed to evaluate the timing of the transition from the treatment cycle of adaptive therapy to high-frequency administration, and to juggle the benefits of intra-competition and killing of the sensitive subpopulation. Based on the simulation and animal experiment, the effectiveness of this method in treating tumors with an aggressive resistant subpopulation has been confirmed. Abstract Adaptive therapy exploits the self-organization of tumor cells to delay the outgrowth of resistant subpopulations successfully. When the tumor has aggressive resistant subpopulations, the outcome of adaptive therapy was not superior to maximum tolerated dose therapy (MTD). To explore methods to improve the adaptive therapy’s performance of this case, the tumor system was constructed by osimertinib-sensitive and resistant cell lines and illustrated by the Lotka-Volterra model in this study. Restore index proposed to assess the system reachability can predict the duration of each treatment cycle. Then the threshold of the restore index was estimated to evaluate the timing of interrupting the treatment cycle and switching to high-frequency administration. The introduced reachability-based adaptive therapy and classic adaptive therapy were compared through simulation and animal experiments. The results suggested that reachability-based adaptive therapy showed advantages when the tumor has an aggressive resistant subpopulation. This study provides a feasible method for evaluating whether to continue the adaptive therapy treatment cycle or switch to high-frequency administration. This method improves the gain of adaptive therapy by taking into account the benefits of tumor intra-competition and the tumor control of killing sensitive subpopulation.
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Babajanyan SG, Lin W, Cheong KH. Cooperate or Not Cooperate in Predictable but Periodically Varying Situations? Cooperation in Fast Oscillating Environment. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2020; 7:2001995. [PMID: 33173734 PMCID: PMC7610311 DOI: 10.1002/advs.202001995] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Revised: 07/03/2020] [Accepted: 07/07/2020] [Indexed: 05/02/2023]
Abstract
In this work, the cooperation problem between two populations in a periodically varying environment is discussed. In particular, the two-population prisoner's dilemma game with periodically oscillating payoffs is discussed, such that the time-average of these oscillations over the period of environmental variations vanishes. The possible overlaps of these oscillations generate completely new dynamical effects that drastically change the phase space structure of the two-population evolutionary dynamics. Due to these effects, the emergence of some level of cooperators in both populations is possible under certain conditions on the environmental variations. In the domain of stable coexistence the dynamics of cooperators in each population form stable cycles. Thus, the cooperators in each population promote the existence of cooperators in the other population. However, the survival of cooperators in both populations is not guaranteed by a large initial fraction of them.
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Affiliation(s)
- S. G. Babajanyan
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design8 Somapah Road S487372Singapore
| | - Wayne Lin
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design8 Somapah Road S487372Singapore
| | - Kang Hao Cheong
- Science, Mathematics and Technology ClusterSingapore University of Technology and Design8 Somapah Road S487372Singapore
- SUTD‐Massachusetts Institute of Technology International Design CentreS487372Singapore
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