1
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Liu J, Li C. Data-driven energy landscape reveals critical genes in cancer progression. NPJ Syst Biol Appl 2024; 10:27. [PMID: 38459043 PMCID: PMC10923824 DOI: 10.1038/s41540-024-00354-4] [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: 11/06/2023] [Accepted: 02/26/2024] [Indexed: 03/10/2024] Open
Abstract
The evolution of cancer is a complex process characterized by stable states and transitions among them. Studying the dynamic evolution of cancer and revealing the mechanisms of cancer progression based on experimental data is an important topic. In this study, we aim to employ a data-driven energy landscape approach to analyze the dynamic evolution of cancer. We take Kidney renal clear cell carcinoma (KIRC) as an example. From the energy landscape, we introduce two quantitative indicators (transition probability and barrier height) to study critical shifts in KIRC cancer evolution, including cancer onset and progression, and identify critical genes involved in these transitions. Our results successfully identify crucial genes that either promote or inhibit these transition processes in KIRC. We also conduct a comprehensive biological function analysis on these genes, validating the accuracy and reliability of our predictions. This work has implications for discovering new biomarkers, drug targets, and cancer treatment strategies in KIRC.
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Affiliation(s)
- Juntan Liu
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, 200433, China
- Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China
| | - Chunhe Li
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, 200433, China.
- Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China.
- School of Mathematical Sciences and MOE Frontiers Center for Brain Science, Fudan University, Shanghai, 200433, China.
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2
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Hu Q, Luo M, Wang R. Identifying critical regulatory interactions in cell fate decision and transition by systematic perturbation analysis. J Theor Biol 2024; 577:111673. [PMID: 37984586 DOI: 10.1016/j.jtbi.2023.111673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2023] [Revised: 11/11/2023] [Accepted: 11/16/2023] [Indexed: 11/22/2023]
Abstract
One of the most significant challenges in biology is to elucidate the roles of various regulatory interactions in cell fate decision and transition. However, it remains to be fully clarified how they cooperate and determine fate transition. Here, a general framework based on statistical analysis and bifurcation theory is proposed to identify crucial regulatory interactions and how they play decisive roles in fate transition. More exactly, specific feedback loops determine occurrence of bifurcations by which cell fate transition can be realized. While regulatory interactions in the feedback loops determine the direction of transition. In addition, two-parameter bifurcation analysis further provides detailed understanding of how the fate transition based on statistical analysis occurs. Statistical analysis can also be used to reveal synergistic combinatorial perturbations by which fate transition can be more efficiently realized. The integrative analysis approach can be used to identify critical regulatory interactions in cell fate transition and reveal how specific cell fate transition occurs. To verify feasibility of the approach, the epithelial to mesenchymal transition (EMT) network is chosen as an illustrative example. In agreement with experimental observations, the approach reveals some critical regulatory interactions and underlying mechanisms in cell fate determination and transitions between three states. The approach can also be applied to analyze other regulatory networks related to cell fate decision and transition.
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Affiliation(s)
- Qing Hu
- Department of Mathematics, Shanghai University, Shanghai, 200444, China
| | - Min Luo
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Ruiqi Wang
- Department of Mathematics, Shanghai University, Shanghai, 200444, China; Newtouch Center for Mathematics of Shanghai University, Shanghai, 200444, China.
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3
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Lv J, Wang J, Li C. Landscape quantifies the intermediate state and transition dynamics in ecological networks. PLoS Comput Biol 2024; 20:e1011766. [PMID: 38181053 PMCID: PMC10796024 DOI: 10.1371/journal.pcbi.1011766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Revised: 01/18/2024] [Accepted: 12/15/2023] [Indexed: 01/07/2024] Open
Abstract
Understanding the ecological mechanisms associated with the collapse and restoration is especially critical in promoting harmonious coexistence between humans and nature. So far, it remains challenging to elucidate the mechanisms of stochastic dynamical transitions for ecological systems. Using an example of plant-pollinator network, we quantified the energy landscape of ecological system. The landscape displays multiple attractors characterizing the high, low and intermediate abundance stable states. Interestingly, we detected the intermediate states under pollinator decline, and demonstrated the indispensable role of the intermediate state in state transitions. From the landscape, we define the barrier height (BH) as a global quantity to evaluate the transition feasibility. We propose that the BH can serve as a new early-warning signal (EWS) for upcoming catastrophic breakdown, which provides an earlier and more accurate warning signal than traditional metrics based on time series. Our results promote developing better management strategies to achieve environmental sustainability.
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Affiliation(s)
- Jinchao Lv
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China
| | - Jin Wang
- Department of Chemistry and of Physics and Astronomy, State University of New York, Stony Brook, New York, United States of America
| | - Chunhe Li
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China
- School of Mathematical Sciences and MOE Frontiers Center for Brain Science, Fudan University, Shanghai, China
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4
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Frank ASJ, Larripa K, Ryu H, Röblitz S. Macrophage phenotype transitions in a stochastic gene-regulatory network model. J Theor Biol 2023; 575:111634. [PMID: 37839584 DOI: 10.1016/j.jtbi.2023.111634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Revised: 08/11/2023] [Accepted: 10/05/2023] [Indexed: 10/17/2023]
Abstract
Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.
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Affiliation(s)
| | - Kamila Larripa
- Department of Mathematics, California State Polytechnic University Humboldt, Arcata, CA, USA.
| | - Hwayeon Ryu
- Department of Mathematics and Statistics, Elon University, Elon, NC, USA.
| | - Susanna Röblitz
- Computational Biology Unit, Department of Informatics, University of Bergen, Bergen, Norway.
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5
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Groves SM, Quaranta V. Quantifying cancer cell plasticity with gene regulatory networks and single-cell dynamics. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1225736. [PMID: 37731743 PMCID: PMC10507267 DOI: 10.3389/fnetp.2023.1225736] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 08/25/2023] [Indexed: 09/22/2023]
Abstract
Phenotypic plasticity of cancer cells can lead to complex cell state dynamics during tumor progression and acquired resistance. Highly plastic stem-like states may be inherently drug-resistant. Moreover, cell state dynamics in response to therapy allow a tumor to evade treatment. In both scenarios, quantifying plasticity is essential for identifying high-plasticity states or elucidating transition paths between states. Currently, methods to quantify plasticity tend to focus on 1) quantification of quasi-potential based on the underlying gene regulatory network dynamics of the system; or 2) inference of cell potency based on trajectory inference or lineage tracing in single-cell dynamics. Here, we explore both of these approaches and associated computational tools. We then discuss implications of each approach to plasticity metrics, and relevance to cancer treatment strategies.
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Affiliation(s)
- Sarah M. Groves
- Department of Pharmacology, Vanderbilt University, Nashville, TN, United States
| | - Vito Quaranta
- Department of Pharmacology, Vanderbilt University, Nashville, TN, United States
- Department of Biochemistry, Vanderbilt University, Nashville, TN, United States
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6
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Proverbio D, Skupin A, Gonçalves J. Systematic analysis and optimization of early warning signals for critical transitions using distribution data. iScience 2023; 26:107156. [PMID: 37456849 PMCID: PMC10338236 DOI: 10.1016/j.isci.2023.107156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/21/2023] [Accepted: 06/12/2023] [Indexed: 07/18/2023] Open
Abstract
Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.
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Affiliation(s)
- Daniele Proverbio
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- National Center for Microscopy and Imaging Research, University of California San Diego, Gilman Drive, La Jolla, CA 9500, USA
- Department of Physics and Material Science, University of Luxembourg, 162a Avenue de La Faiencerie, 1511 Luxembourg, Luxembourg
| | - Jorge Gonçalves
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
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7
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Ji P, Wang Y, Peron T, Li C, Nagler J, Du J. Structure and function in artificial, zebrafish and human neural networks. Phys Life Rev 2023; 45:74-111. [PMID: 37182376 DOI: 10.1016/j.plrev.2023.04.004] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 04/20/2023] [Indexed: 05/16/2023]
Abstract
Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.
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Affiliation(s)
- Peng Ji
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China; Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence, Ministry of Education, Shanghai 200433, China; MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China
| | - Yufan Wang
- Institute of Neuroscience, State Key Laboratory of Neuroscience, Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, 320 Yue-Yang Road, Shanghai 200031, China
| | - Thomas Peron
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos 13566-590, São Paulo, Brazil.
| | - Chunhe Li
- Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, Shanghai 200433, China; Institute of Science and Technology for Brain-Inspired Intelligence and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China.
| | - Jan Nagler
- Deep Dynamics, Frankfurt School of Finance & Management, Frankfurt, Germany; Centre for Human and Machine Intelligence, Frankfurt School of Finance & Management, Frankfurt, Germany
| | - Jiulin Du
- Institute of Neuroscience, State Key Laboratory of Neuroscience, Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, 320 Yue-Yang Road, Shanghai 200031, China.
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8
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Bian S, Zhang Y, Li C. An improved approach for calculating energy landscape of gene networks from moment equations. CHAOS (WOODBURY, N.Y.) 2023; 33:023116. [PMID: 36859199 DOI: 10.1063/5.0128345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
The energy landscape theory has widely been applied to study the stochastic dynamics of biological systems. Different methods have been developed to quantify the energy landscape for gene networks, e.g., using Gaussian approximation (GA) approach to calculate the landscape by solving the diffusion equation approximately from the first two moments. However, how high-order moments influence the landscape construction remains to be elucidated. Also, multistability exists extensively in biological networks. So, how to quantify the landscape for a multistable dynamical system accurately, is a paramount problem. In this work, we prove that the weighted summation from GA (WSGA), provides an effective way to calculate the landscape for multistable systems and limit cycle systems. Meanwhile, we proposed an extended Gaussian approximation (EGA) approach by considering the effects of the third moments, which provides a more accurate way to obtain probability distribution and corresponding landscape. By applying our generalized EGA approach to two specific biological systems: multistable genetic circuit and synthetic oscillatory network, we compared EGA with WSGA by calculating the KL divergence of the probability distribution between these two approaches and simulations, which demonstrated that the EGA provides a more accurate approach to calculate the energy landscape.
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Affiliation(s)
- Shirui Bian
- School of Mathematical Sciences, Fudan University, Shanghai 200433, China
| | - Yunxin Zhang
- School of Mathematical Sciences, Fudan University, Shanghai 200433, China
| | - Chunhe Li
- School of Mathematical Sciences, Fudan University, Shanghai 200433, China
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9
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Burger GA, Nesenberend DN, Lems CM, Hille SC, Beltman JB. Bidirectional crosstalk between epithelial-mesenchymal plasticity and IFN γ-induced PD-L1 expression promotes tumour progression. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220186. [PMID: 36397970 PMCID: PMC9626257 DOI: 10.1098/rsos.220186] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Accepted: 10/05/2022] [Indexed: 06/16/2023]
Abstract
Epithelial-mesenchymal transition (EMT) and immunoevasion through upregulation of programmed death-ligand 1 (PD-L1) are important drivers of cancer progression. While EMT has been proposed to facilitate PD-L1-mediated immunosuppression, molecular mechanisms of their interaction remain obscure. Here, we provide insight into these mechanisms by proposing a mathematical model that describes the crosstalk between EMT and interferon gamma (IFNγ)-induced PD-L1 expression. Our model shows that via interaction with microRNA-200 (miR-200), the multi-stability of the EMT regulatory circuit is mirrored in PD-L1 levels, which are further amplified by IFNγ stimulation. This IFNγ-mediated effect is most prominent for cells in a fully mesenchymal state and less strong for those in an epithelial or partially mesenchymal state. In addition, bidirectional crosstalk between miR-200 and PD-L1 implies that IFNγ stimulation allows cells to undergo EMT for lower amounts of inducing signal, and the presence of IFNγ accelerates EMT and decelerates mesenchymal-epithelial transition (MET). Overall, our model agrees with published findings and provides insight into possible mechanisms behind EMT-mediated immune evasion, and primary, adaptive, or acquired resistance to immunotherapy. Our model can be used as a starting point to explore additional crosstalk mechanisms, as an improved understanding of these mechanisms is indispensable for developing better diagnostic and therapeutic options for cancer patients.
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Affiliation(s)
- Gerhard A. Burger
- Division of Drug Discovery and Safety, Leiden University, Leiden, The Netherlands
| | - Daphne N. Nesenberend
- Division of Drug Discovery and Safety, Leiden University, Leiden, The Netherlands
- Mathematical Institute, Leiden Academic Centre for Drug Research, Leiden University, Leiden, The Netherlands
| | - Carlijn M. Lems
- Division of Drug Discovery and Safety, Leiden University, Leiden, The Netherlands
| | - Sander C. Hille
- Mathematical Institute, Leiden Academic Centre for Drug Research, Leiden University, Leiden, The Netherlands
| | - Joost B. Beltman
- Division of Drug Discovery and Safety, Leiden University, Leiden, The Netherlands
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10
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Cancer: More than a geneticist’s Pandora’s box. J Biosci 2022. [DOI: 10.1007/s12038-022-00254-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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11
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Bongrand P. Is There a Need for a More Precise Description of Biomolecule Interactions to Understand Cell Function? Curr Issues Mol Biol 2022; 44:505-525. [PMID: 35723321 PMCID: PMC8929073 DOI: 10.3390/cimb44020035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Revised: 01/15/2022] [Accepted: 01/17/2022] [Indexed: 11/16/2022] Open
Abstract
An important goal of biological research is to explain and hopefully predict cell behavior from the molecular properties of cellular components. Accordingly, much work was done to build extensive “omic” datasets and develop theoretical methods, including computer simulation and network analysis to process as quantitatively as possible the parameters contained in these resources. Furthermore, substantial effort was made to standardize data presentation and make experimental results accessible to data scientists. However, the power and complexity of current experimental and theoretical tools make it more and more difficult to assess the capacity of gathered parameters to support optimal progress in our understanding of cell function. The purpose of this review is to focus on biomolecule interactions, the interactome, as a specific and important example, and examine the limitations of the explanatory and predictive power of parameters that are considered as suitable descriptors of molecular interactions. Recent experimental studies on important cell functions, such as adhesion and processing of environmental cues for decision-making, support the suggestion that it should be rewarding to complement standard binding properties such as affinity and kinetic constants, or even force dependence, with less frequently used parameters such as conformational flexibility or size of binding molecules.
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Affiliation(s)
- Pierre Bongrand
- Lab Adhesion and Inflammation (LAI), Inserm UMR 1067, Cnrs UMR 7333, Aix-Marseille Université UM 61, Marseille 13009, France
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12
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Mertins SD. Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning. Front Oncol 2022; 11:805592. [PMID: 35127516 PMCID: PMC8813744 DOI: 10.3389/fonc.2021.805592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Accepted: 12/31/2021] [Indexed: 12/02/2022] Open
Abstract
Computational dynamic ODE models of cell function describing biochemical reactions have been created for decades, but on a small scale. Still, they have been highly effective in describing and predicting behaviors. For example, oscillatory phospho-ERK levels were predicted and confirmed in MAPK signaling encompassing both positive and negative feedback loops. These models typically were limited and not adapted to large datasets so commonly found today. But importantly, ODE models describe reaction networks in well-mixed systems representing the cell and can be simulated with ordinary differential equations that are solved deterministically. Stochastic solutions, which can account for noisy reaction networks, in some cases, also improve predictions. Today, dynamic ODE models rarely encompass an entire cell even though it might be expected that an upload of the large genomic, transcriptomic, and proteomic datasets may allow whole cell models. It is proposed here to combine output from simulated dynamic ODE models, completed with omics data, to discover both biomarkers in cancer a priori and molecular targets in the Machine Learning setting.
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Affiliation(s)
- Susan D. Mertins
- Department of Science, Mount St. Mary’s University, Emmitsburg, MD, United States
- Biomedical Informatics and Data Science Directorate, Frederick National Laboratory for Cancer Research, Leidos Biomedical Research, Limited Liability Company (LLC), Frederick, MD, United States
- BioSystems Strategies, Limited Liability Company (LLC), Frederick, MD, United States
- *Correspondence: Susan D. Mertins,
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13
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Lang J, Li C. Unraveling the stochastic transition mechanism between oscillation states by landscape and minimum action path theory. Phys Chem Chem Phys 2022; 24:20050-20063. [DOI: 10.1039/d2cp01385a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Cell fate transitions have been studied from various perspectives, such as the transition between stable states, or the transition between stable states and oscillation states. However, there is a lack...
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14
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Yang X, Luo S, Zhang Z, Wang Z, Zhou T, Zhang J. Silent transcription intervals and translational bursting lead to diverse phenotypic switching. Phys Chem Chem Phys 2022; 24:26600-26608. [DOI: 10.1039/d2cp03703c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
For complex process of gene expression, we use theoretical analysis and stochastic simulations to study the phenotypic diversity induced by silent transcription intervals and translational bursting.
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Affiliation(s)
- Xiyan Yang
- School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, P. R. China
| | - Songhao Luo
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Zhenquan Zhang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Zihao Wang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Tianshou Zhou
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Jiajun Zhang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
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15
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Jiang Q, Zhang S, Wan L. Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data. PLoS Comput Biol 2022; 18:e1009821. [PMID: 35073331 PMCID: PMC8812873 DOI: 10.1371/journal.pcbi.1009821] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2021] [Revised: 02/03/2022] [Accepted: 01/10/2022] [Indexed: 12/27/2022] Open
Abstract
Time series single-cell RNA sequencing (scRNA-seq) data are emerging. However, dynamic inference of an evolving cell population from time series scRNA-seq data is challenging owing to the stochasticity and nonlinearity of the underlying biological processes. This calls for the development of mathematical models and methods capable of reconstructing cellular dynamic transition processes and uncovering the nonlinear cell-cell interactions. In this study, we present GraphFP, a nonlinear Fokker-Planck equation on graph based model and dynamic inference framework, with the aim of reconstructing the cell state-transition complex potential energy landscape from time series single-cell transcriptomic data. The free energy of our model explicitly takes into account of the cell-cell interactions in a nonlinear quadratic term. We then recast the model inference problem in the form of a dynamic optimal transport framework and solve it efficiently with the adjoint method of optimal control. We evaluated GraphFP on the time series scRNA-seq data set of embryonic murine cerebral cortex development. We illustrated that it 1) reconstructs cell state potential energy, which is a measure of cellular differentiation potency, 2) faithfully charts the probability flows between paired cell states over the dynamic processes of cell differentiation, and 3) accurately quantifies the stochastic dynamics of cell type frequencies on probability simplex in continuous time. We also illustrated that GraphFP is robust in terms of cluster labelling with different resolutions, as well as parameter choices. Meanwhile, GraphFP provides a model-based approach to delineate the cell-cell interactions that drive cell differentiation. GraphFP software is available at https://github.com/QiJiang-QJ/GraphFP. Dynamic inference of cell development processes from time series scRNA-seq data is a major challenge. Here, we present GraphFP, a coherent computational framework that simultaneously reconstructs the cell state-transition complex potential energy landscape and infers cell-cell interactions from time series single-cell transcriptomic data. Based on the mathematical framework of nonlinear Fokker-Planck equation on graph, GraphFP models the stochastic dynamics of the cell state/type frequencies on probability simplex in continuous time, where the free energy with a nonlinear quadratic interaction term is employed to characterize cell-cell interactions. We formulate the model inference problem in the form of a dynamic optimal transport framework and solve it efficiently with the celebrated adjoint method. GraphFP allows for 1) reconstructing cell state potential energy, which is a measure of cellular differentiation potency, 2) charting the probability flows between paired cell states over dynamic processes, 3) quantifying the stochastic dynamics of cell type frequencies on probability simplex in continuous time, and 4) delineating cell-cell interactions that drive cell differentiation. We show how GraphFP can be used to faithfully reveal and accurately quantify the cell development processes using the embryonic murine cerebral cortex development time series scRNA-seq dataset.
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Affiliation(s)
- Qi Jiang
- NCMIS, LSC, LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Shuo Zhang
- NCMIS, LSC, LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Lin Wan
- NCMIS, LSC, LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China
- * E-mail:
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16
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Murugan R, Kreiman G. Multiple transcription auto regulatory loops can act as robust oscillators and decision-making motifs. Comput Struct Biotechnol J 2022; 20:5115-5135. [PMID: 36187915 PMCID: PMC9493064 DOI: 10.1016/j.csbj.2022.08.065] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Revised: 08/28/2022] [Accepted: 08/30/2022] [Indexed: 11/29/2022] Open
Abstract
We have shown that: Negative transcription auto regulation can speed up the response time at the cost of reduced steady state protein levels. Under strong binding conditions, one can increase the steady state protein level by increasing the gene copy number without a compromise on the response time. Multiple negative transcription autoregulatory motifs can be tuned for both the response time as well as steady state protein levels by varying the gene copy number. Multiple negative autoregulatory loops can act as robust genetic oscillators. Dual feedback motifs constructed with multiple negative and positive autoregulatory loop components can act as robust oscillators and bistable decision making units within the transcription factor networks.
Response time decides how fast a gene can react against an external signal at the transcription level in a signalling cascade. The steady state protein levels of the responding genes decide the coupling between two consecutive members of a signalling cascade. A negative autoregulatory loop (NARL) present in a transcription factor network can speed up the response time of the regulated gene at the cost of reduced steady state protein level. We present here a multi NARL motif which can be tuned for both the steady state protein level as well as response time in the required direction. Remarkably, there exists an optimum Hill coefficient nopt≅4 at which the response time of the NARL motif is at minimum. When the Hill coefficient is n < nopt, then under strong binding conditions, one can raise the steady state protein level by increasing the gene copy number with almost no change in the response time of the multi NARL motif. Using detailed computational analysis, we show that the coupled multi NARL and positive auto regulatory loop (PARL) motifs can act as an oscillator as well as decision making component which are robust against extrinsic fluctuations in the control parameters. We further demonstrate that the period of oscillation of the coupled multi NARL-PARL dual feedback oscillator can also be fine-tuned by the gene copy number apart from the inducer concentration. We finally demonstrate robustness of bistable dual feedback decision making motifs with multi autoregulatory loop component.
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Affiliation(s)
- Rajamanickam Murugan
- Department of Biotechnology, Indian Institute of Technology Madras, Chennai 600036, India
| | - Gabriel Kreiman
- Children’s Hospital Boston, Harvard Medical School, Boston, USA
- Corresponding author at: Children’s Hospital Boston, Harvard Medical School, Boston, USA.
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17
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Li X, Li T, Li C, Li T. Uncovering the cell fate decision in lysis-lysogeny transition and stem cell development via Markov state modeling. J Chem Phys 2021; 155:245101. [PMID: 34972376 DOI: 10.1063/5.0070485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Understanding the behavior of a complex gene regulatory network is a fundamental but challenging task in systems biology. How to reduce the large number of degrees of freedom of a specific network and identify its main biological pathway is the key issue. In this paper, we utilized the transition path theory (TPT) and Markov state modeling (MSM) framework to numerically study two typical cell fate decision processes: the lysis-lysogeny transition and stem cell development. The application of TPT to the lysis-lysogeny decision-making system reveals that the competitions of CI and Cro dimer binding play the major role in determining the cell fates. We also quantified the transition rates from the lysogeny to lysis state under different conditions. The overall computational results are consistent with biological intuitions but with more detailed information. For the stem cell developmental system, we applied the MSM to reduce the original dynamics to a moderate-size Markov chain. Further spectral analysis showed that the reduced system exhibits nine metastable states, which correspond to the refinement of the five known typical cell types in development. We further investigated the dominant transition pathways corresponding to the cell differentiation, reprogramming, and trans-differentiation. A similar approach can be applied to study other biological systems.
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Affiliation(s)
- Xiaoguang Li
- MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, People's Republic of China
| | - Tongkai Li
- LMAM and School of Mathematical Sciences, Peking University, Beijing, China
| | - Chunhe Li
- Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, Shanghai, China
| | - Tiejun Li
- LMAM and School of Mathematical Sciences, Peking University, Beijing, China
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18
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Mandal S, Tejaswi T, Janivara R, Srikrishnan S, Thakur P, Sahoo S, Chakraborty P, Sohal SS, Levine H, George JT, Jolly MK. Transcriptomic-Based Quantification of the Epithelial-Hybrid-Mesenchymal Spectrum across Biological Contexts. Biomolecules 2021; 12:29. [PMID: 35053177 PMCID: PMC8773604 DOI: 10.3390/biom12010029] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Revised: 12/20/2021] [Accepted: 12/21/2021] [Indexed: 12/12/2022] Open
Abstract
Epithelial-mesenchymal plasticity (EMP) underlies embryonic development, wound healing, and cancer metastasis and fibrosis. Cancer cells exhibiting EMP often have more aggressive behavior, characterized by drug resistance, and tumor-initiating and immuno-evasive traits. Thus, the EMP status of cancer cells can be a critical indicator of patient prognosis. Here, we compare three distinct transcriptomic-based metrics-each derived using a different gene list and algorithm-that quantify the EMP spectrum. Our results for over 80 cancer-related RNA-seq datasets reveal a high degree of concordance among these metrics in quantifying the extent of EMP. Moreover, each metric, despite being trained on cancer expression profiles, recapitulates the expected changes in EMP scores for non-cancer contexts such as lung fibrosis and cellular reprogramming into induced pluripotent stem cells. Thus, we offer a scoring platform to quantify the extent of EMP in vitro and in vivo for diverse biological applications including cancer.
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Affiliation(s)
- Susmita Mandal
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India; (S.M.); (T.T.); (S.S.); (P.C.)
| | - Tanishq Tejaswi
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India; (S.M.); (T.T.); (S.S.); (P.C.)
- Undergraduate Programme, Indian Institute of Science, Bangalore 560012, India
| | - Rohini Janivara
- Department of Biological Sciences, Georgia Institute of Technology, Atlanta, GA 30332, USA;
| | - Syamanthak Srikrishnan
- Department of Biotechnology, Indian Institute of Technology, Kharagpur 721302, India; (S.S.); (P.T.)
| | - Pradipti Thakur
- Department of Biotechnology, Indian Institute of Technology, Kharagpur 721302, India; (S.S.); (P.T.)
| | - Sarthak Sahoo
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India; (S.M.); (T.T.); (S.S.); (P.C.)
| | - Priyanka Chakraborty
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India; (S.M.); (T.T.); (S.S.); (P.C.)
| | - Sukhwinder Singh Sohal
- Respiratory Translational Research Group, Department of Laboratory Medicine, School of Health Sciences, College of Health and Medicine, University of Tasmania, Launceston 7248, Australia;
| | - Herbert Levine
- Departments of Physics and Bioengineering, Northeastern University, Boston, MA 02115, USA;
- Center for Theoretical Biological Physics, Rice University, Houston, TX 77030, USA
| | - Jason T. George
- Center for Theoretical Biological Physics, Rice University, Houston, TX 77030, USA
| | - Mohit Kumar Jolly
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India; (S.M.); (T.T.); (S.S.); (P.C.)
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