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Gare S, Chel S, Abhinav TK, Dhyani V, Jana S, Giri L. Mapping of structural arrangement of cells and collective calcium transients: an integrated framework combining live cell imaging using confocal microscopy and UMAP-assisted HDBSCAN-based approach. Integr Biol (Camb) 2022; 14:184-203. [PMID: 36670549 DOI: 10.1093/intbio/zyac017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Revised: 11/22/2022] [Accepted: 11/30/2022] [Indexed: 01/22/2023]
Abstract
Live cell calcium (Ca2+) imaging is one of the important tools to record cellular activity during in vitro and in vivo preclinical studies. Specially, high-resolution microscopy can provide valuable dynamic information at the single cell level. One of the major challenges in the implementation of such imaging schemes is to extract quantitative information in the presence of significant heterogeneity in Ca2+ responses attained due to variation in structural arrangement and drug distribution. To fill this gap, we propose time-lapse imaging using spinning disk confocal microscopy and machine learning-enabled framework for automated grouping of Ca2+ spiking patterns. Time series analysis is performed to correlate the drug induced cellular responses to self-assembly pattern present in multicellular systems. The framework is designed to reduce the large-scale dynamic responses using uniform manifold approximation and projection (UMAP). In particular, we propose the suitability of hierarchical DBSCAN (HDBSCAN) in view of reduced number of hyperparameters. We find UMAP-assisted HDBSCAN outperforms existing approaches in terms of clustering accuracy in segregation of Ca2+ spiking patterns. One of the novelties includes the application of non-linear dimension reduction in segregation of the Ca2+ transients with statistical similarity. The proposed pipeline for automation was also proved to be a reproducible and fast method with minimal user input. The algorithm was used to quantify the effect of cellular arrangement and stimulus level on collective Ca2+ responses induced by GPCR targeting drug. The analysis revealed a significant increase in subpopulation containing sustained oscillation corresponding to higher packing density. In contrast to traditional measurement of rise time and decay ratio from Ca2+ transients, the proposed pipeline was used to classify the complex patterns with longer duration and cluster-wise model fitting. The two-step process has a potential implication in deciphering biophysical mechanisms underlying the Ca2+ oscillations in context of structural arrangement between cells.
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Affiliation(s)
- Suman Gare
- Department of Chemical Engineering, Indian Institute of Technology, Hyderabad, India
| | - Soumita Chel
- Department of Chemical Engineering, Indian Institute of Technology, Hyderabad, India
| | - T K Abhinav
- Department of Chemical Engineering, Indian Institute of Technology, Hyderabad, India
| | - Vaibhav Dhyani
- Department of Chemical Engineering, Indian Institute of Technology, Hyderabad, India
| | - Soumya Jana
- Department of Electrical Engineering, Indian Institute of Technology, Hyderabad, India
| | - Lopamudra Giri
- Department of Chemical Engineering, Indian Institute of Technology, Hyderabad, India
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2
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Sinha N, Yang H, Janse D, Hendriks L, Rand U, Hauser H, Köster M, van de Vosse FN, de Greef TFA, Tel J. Microfluidic chip for precise trapping of single cells and temporal analysis of signaling dynamics. COMMUNICATIONS ENGINEERING 2022; 1:18. [PMCID: PMC10955935 DOI: 10.1038/s44172-022-00019-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2022] [Accepted: 07/12/2022] [Indexed: 06/15/2024]
Abstract
Microfluidic designs are versatile examples of technology miniaturisation that find their applications in various cell biology research, especially to investigate the influence of environmental signals on cellular response dynamics. Multicellular systems operate in intricate cellular microenvironments where environmental signals govern well-orchestrated and robust responses, the understanding of which can be realized with integrated microfluidic systems. In this study, we present a fully automated and integrated microfluidic chip that can deliver input signals to single and isolated suspension or adherent cells in a precisely controlled manner. In respective analyses of different single cell types, we observe, in real-time, the temporal dynamics of caspase 3 activation during DMSO-induced apoptosis in single cancer cells (K562) and the translocation of STAT-1 triggered by interferon γ (IFNγ) in single fibroblasts (NIH3T3). Our investigations establish the employment of our versatile microfluidic system in probing temporal single cell signaling networks where alternations in outputs uncover signal processing mechanisms. Nidhi Sinha, Haowen Yang and colleagues report a microfluidic large-scale integration chip to probe temporal single-cell signalling networks via the delivery of patterns of input signalling molecules. The researchers use their device to investigate drug-induced cancer cell apoptosis and single cell transcription (STAT-1) protein signalling dynamics.
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Affiliation(s)
- Nidhi Sinha
- Laboratory of Immunoengineering, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
- Institute of Complex Molecular Systems, TU Eindhoven, 5600 MB Eindhoven, Netherlands
| | - Haowen Yang
- Laboratory of Immunoengineering, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
- Institute of Complex Molecular Systems, TU Eindhoven, 5600 MB Eindhoven, Netherlands
| | - David Janse
- Laboratory of Immunoengineering, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
| | - Luc Hendriks
- Laboratory of Immunoengineering, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
| | - Ulfert Rand
- Model Systems for Infection and Immunity, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany
| | - Hansjörg Hauser
- Model Systems for Infection and Immunity, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany
| | - Mario Köster
- Model Systems for Infection and Immunity, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany
| | - Frans N. van de Vosse
- Cardiovascular Biomechanics Group, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
| | - Tom F. A. de Greef
- Institute of Complex Molecular Systems, TU Eindhoven, 5600 MB Eindhoven, Netherlands
- Computational Biology Group, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
| | - Jurjen Tel
- Laboratory of Immunoengineering, Department of Biomedical Engineering, TU Eindhoven, 5600 MB Eindhoven, Netherlands
- Institute of Complex Molecular Systems, TU Eindhoven, 5600 MB Eindhoven, Netherlands
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Patel P, Drayman N, Liu P, Bilgic M, Tay S. Computer vision reveals hidden variables underlying NF-κB activation in single cells. SCIENCE ADVANCES 2021; 7:eabg4135. [PMID: 34678061 PMCID: PMC8535821 DOI: 10.1126/sciadv.abg4135] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 09/02/2021] [Indexed: 05/31/2023]
Abstract
Individual cells are heterogeneous when responding to environmental cues. Under an external signal, certain cells activate gene regulatory pathways, while others completely ignore that signal. Mechanisms underlying cellular heterogeneity are often inaccessible because experiments needed to study molecular states destroy the very states that we need to examine. Here, we developed an image-based support vector machine learning model to uncover variables controlling activation of the immune pathway nuclear factor κB (NF-κB). Computer vision analysis predicts the identity of cells that will respond to cytokine stimulation and shows that activation is predetermined by minute amounts of “leaky” NF-κB (p65:p50) localization to the nucleus. Mechanistic modeling revealed that the ratio of NF-κB to inhibitor of NF-κB predetermines leakiness and activation probability of cells. While cells transition between molecular states, they maintain their overall probabilities for NF-κB activation. Our results demonstrate how computer vision can find mechanisms behind heterogeneous single-cell activation under proinflammatory stimuli.
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Affiliation(s)
- Parthiv Patel
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA
- Institute for Genomics and Systems Biology, The University of Chicago, Chicago, IL, USA
| | - Nir Drayman
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA
- Institute for Genomics and Systems Biology, The University of Chicago, Chicago, IL, USA
| | - Ping Liu
- Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA
| | - Mustafa Bilgic
- Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA
| | - Savaş Tay
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA
- Institute for Genomics and Systems Biology, The University of Chicago, Chicago, IL, USA
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4
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Cruz JA, Mokashi CS, Kowalczyk GJ, Guo Y, Zhang Q, Gupta S, Schipper DL, Smeal SW, Lee REC. A variable-gain stochastic pooling motif mediates information transfer from receptor assemblies into NF-κB. SCIENCE ADVANCES 2021; 7:7/30/eabi9410. [PMID: 34301608 PMCID: PMC8302133 DOI: 10.1126/sciadv.abi9410] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 06/04/2021] [Indexed: 06/13/2023]
Abstract
A myriad of inflammatory cytokines regulate signaling pathways to maintain cellular homeostasis. The IκB kinase (IKK) complex is an integration hub for cytokines that govern nuclear factor κB (NF-κB) signaling. In response to inflammation, IKK is activated through recruitment to receptor-associated protein assemblies. How and what information IKK complexes transmit about the milieu are open questions. Here, we track dynamics of IKK complexes and nuclear NF-κB to identify upstream signaling features that determine same-cell responses. Experiments and modeling of single complexes reveal their size, number, and timing relays cytokine-specific control over shared signaling mechanisms with feedback regulation that is independent of transcription. Our results provide evidence for variable-gain stochastic pooling, a noise-reducing motif that enables cytokine-specific regulation and parsimonious information transfer. We propose that emergent properties of stochastic pooling are general principles of receptor signaling that have evolved for constructive information transmission in noisy molecular environments.
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Affiliation(s)
- J Agustin Cruz
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - Chaitanya S Mokashi
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - Gabriel J Kowalczyk
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - Yue Guo
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Qiuhong Zhang
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - Sanjana Gupta
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - David L Schipper
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - Steven W Smeal
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA
| | - Robin E C Lee
- Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA.
- Center for Systems Immunology, University of Pittsburgh School of Medicine, Pittsburgh, PA 15213, USA
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5
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Kinnunen PC, Luker KE, Luker GD, Linderman JJ. Computational methods for characterizing and learning from heterogeneous cell signaling data. CURRENT OPINION IN SYSTEMS BIOLOGY 2021; 26:98-108. [PMID: 35647414 DOI: 10.1016/j.coisb.2021.04.009] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Heterogeneity in cell signaling pathways is increasingly appreciated as a fundamental feature of cell biology and a driver of clinically relevant disease phenotypes. Understanding the causes of heterogeneity, the cellular mechanisms used to control heterogeneity, and the downstream effects of heterogeneity in single cells are all key obstacles for manipulating cellular populations and treating disease. Recent advances in genetic engineering, including multiplexed fluorescent reporters, have provided unprecedented measurements of signaling heterogeneity, but these vast data sets are often difficult to interpret, necessitating the use of computational techniques to extract meaning from the data. Here, we review recent advances in computational methods for extracting meaning from these novel data streams. In particular, we evaluate how machine learning methods related to dimensionality reduction and classification can identify structure in complex, dynamic datasets, simplifying interpretation. We also discuss how mechanistic models can be merged with heterogeneous data to understand the underlying differences between cells in a population. These methods are still being developed, but the work reviewed here offers useful applications of specific analysis techniques that could enable the translation of single-cell signaling data to actionable biological understanding.
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Affiliation(s)
- Patrick C Kinnunen
- Department of Chemical Engineering, University of Michigan, 2800 Plymouth Road, Ann Arbor, MI, 48109-2800, USA
| | - Kathryn E Luker
- Department of Radiology, Center for Molecular Imaging, University of Michigan, 109 Zina Pitcher Place, A526 BSRB, Ann Arbor, MI, 48109-2200, USA
| | - Gary D Luker
- Department of Radiology, Center for Molecular Imaging, University of Michigan, 109 Zina Pitcher Place, A526 BSRB, Ann Arbor, MI, 48109-2200, USA.,Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI, USA, 48109.,Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI, USA, 48109
| | - Jennifer J Linderman
- Department of Chemical Engineering, University of Michigan, 2800 Plymouth Road, Ann Arbor, MI, 48109-2800, USA.,Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI, USA, 48109
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6
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Pomeroy AE, Peña MI, Houser JR, Dixit G, Dohlman HG, Elston TC, Errede B. A predictive model of gene expression reveals the role of network motifs in the mating response of yeast. Sci Signal 2021; 14:14/670/eabb5235. [PMID: 33593998 DOI: 10.1126/scisignal.abb5235] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Cells use signaling pathways to receive and process information about their environment. These nonlinear systems rely on feedback and feedforward regulation to respond appropriately to changing environmental conditions. Mathematical models describing signaling pathways often lack predictive power because they are not trained on data that encompass the diverse time scales on which these regulatory mechanisms operate. We addressed this limitation by measuring transcriptional changes induced by the mating response in Saccharomyces cerevisiae exposed to different dynamic patterns of pheromone. We found that pheromone-induced transcription persisted after pheromone removal and showed long-term adaptation upon sustained pheromone exposure. We developed a model of the regulatory network that captured both characteristics of the mating response. We fit this model to experimental data with an evolutionary algorithm and used the parameterized model to predict scenarios for which it was not trained, including different temporal stimulus profiles and genetic perturbations to pathway components. Our model allowed us to establish the role of four architectural elements of the network in regulating gene expression. These network motifs are incoherent feedforward, positive feedback, negative feedback, and repressor binding. Experimental and computational perturbations to these network motifs established a specific role for each in coordinating the mating response to persistent and dynamic stimulation.
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Affiliation(s)
- Amy E Pomeroy
- Curriculum in Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
| | - Matthew I Peña
- Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
| | - John R Houser
- Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Gauri Dixit
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Henrik G Dohlman
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Timothy C Elston
- Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA. .,Computational Medicine Program, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Beverly Errede
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
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7
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Spinosa PC, Kinnunen PC, Humphries BA, Luker GD, Luker KE, Linderman JJ. Pre-existing Cell States Control Heterogeneity of Both EGFR and CXCR4 Signaling. Cell Mol Bioeng 2021; 14:49-64. [PMID: 33643466 PMCID: PMC7878609 DOI: 10.1007/s12195-020-00640-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 07/22/2020] [Indexed: 10/23/2022] Open
Abstract
INTRODUCTION CXCR4 and epidermal growth factor receptor (EGFR) represent two major families of receptors, G-protein coupled receptors and receptor tyrosine kinases, with central functions in cancer. While utilizing different upstream signaling molecules, both CXCR4 and EGFR activate kinases ERK and Akt, although single-cell activation of these kinases is markedly heterogeneous. One hypothesis regarding the origin of signaling heterogeneity proposes that intercellular variations arise from differences in pre-existing intracellular states set by extrinsic noise. While pre-existing cell states vary among cells, each pre-existing state defines deterministic signaling outputs to downstream effectors. Understanding causes of signaling heterogeneity will inform treatment of cancers with drugs targeting drivers of oncogenic signaling. METHODS We built a single-cell computational model to predict Akt and ERK responses to CXCR4- and EGFR-mediated stimulation. We investigated signaling heterogeneity through these receptors and tested model predictions using quantitative, live-cell time-lapse imaging. RESULTS We show that the pre-existing cell state predicts single-cell signaling through both CXCR4 and EGFR. Computational modeling reveals that the same set of pre-existing cell states explains signaling heterogeneity through both EGFR and CXCR4 at multiple doses of ligands and in two different breast cancer cell lines. The model also predicts how phosphatidylinositol-3-kinase (PI3K) targeted therapies potentiate ERK signaling in certain breast cancer cells and that low level, combined inhibition of MEK and PI3K ablates potentiated ERK signaling. CONCLUSIONS Our data demonstrate that a conserved motif exists for EGFR and CXCR4 signaling and suggest potential clinical utility of the computational model to optimize therapy.
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Affiliation(s)
- Phillip C. Spinosa
- Department of Chemical Engineering, University of Michigan, 2800 Plymouth Road, Ann Arbor, MI 48109-2800 USA
| | - Patrick C. Kinnunen
- Department of Chemical Engineering, University of Michigan, 2800 Plymouth Road, Ann Arbor, MI 48109-2800 USA
| | - Brock A. Humphries
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109 USA
| | - Gary D. Luker
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109 USA
- Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI USA 48109
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI USA 48109
| | - Kathryn E. Luker
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109 USA
- Department of Radiology, Center for Molecular Imaging, University of Michigan, 109 Zina Pitcher Place, A526 BSRB, Ann Arbor, MI 48109-2200 USA
| | - Jennifer J. Linderman
- Department of Chemical Engineering, University of Michigan, 2800 Plymouth Road, Ann Arbor, MI 48109-2800 USA
- Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI USA 48109
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Spinosa PC, Humphries BA, Lewin Mejia D, Buschhaus JM, Linderman JJ, Luker GD, Luker KE. Short-term cellular memory tunes the signaling responses of the chemokine receptor CXCR4. Sci Signal 2019; 12:eaaw4204. [PMID: 31289212 PMCID: PMC7059217 DOI: 10.1126/scisignal.aaw4204] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The chemokine receptor CXCR4 regulates fundamental processes in development, normal physiology, and diseases, including cancer. Small subpopulations of CXCR4-positive cells drive the local invasion and dissemination of malignant cells during metastasis, emphasizing the need to understand the mechanisms controlling responses at the single-cell level to receptor activation by the chemokine ligand CXCL12. Using single-cell imaging, we discovered that short-term cellular memory of changes in environmental conditions tuned CXCR4 signaling to Akt and ERK, two kinases activated by this receptor. Conditioning cells with growth stimuli before CXCL12 exposure increased the number of cells that initiated CXCR4 signaling and the amplitude of Akt and ERK activation. Data-driven, single-cell computational modeling revealed that growth factor conditioning modulated CXCR4-dependent activation of Akt and ERK by decreasing extrinsic noise (preexisting cell-to-cell differences in kinase activity) in PI3K and mTORC1. Modeling established mTORC1 as critical for tuning single-cell responses to CXCL12-CXCR4 signaling. Our single-cell model predicted how combinations of extrinsic noise in PI3K, Ras, and mTORC1 superimposed on different driver mutations in the ERK and/or Akt pathways to bias CXCR4 signaling. Computational experiments correctly predicted that selected kinase inhibitors used for cancer therapy shifted subsets of cells to states that were more permissive to CXCR4 activation, suggesting that such drugs may inadvertently potentiate pro-metastatic CXCR4 signaling. Our work establishes how changing environmental inputs modulate CXCR4 signaling in single cells and provides a framework to optimize the development and use of drugs targeting this signaling pathway.
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Affiliation(s)
- Phillip C Spinosa
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
| | - Brock A Humphries
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109, USA
| | - Daniela Lewin Mejia
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109, USA
| | - Johanna M Buschhaus
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109, USA
- Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI 48109, USA
| | - Jennifer J Linderman
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
- Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI 48109, USA
| | - Gary D Luker
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109, USA.
- Department of Biomedical Engineering, University of Michigan Medical School, Ann Arbor, MI 48109, USA
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109, USA
| | - Kathryn E Luker
- Department of Radiology Center for Molecular Imaging, University of Michigan Medical School, Ann Arbor, MI 48109, USA.
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