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  • Letter
  • Open Access

Cellular gradient flow structure linking single-cell-level rules and population-level dynamics

Shuhei A. Horiguchi and Tetsuya J. Kobayashi*

  • Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

  • *Also at Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba Meguro-ku, Tokyo 153-8505, Japan; tetsuya@mail.crmind.net
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Phys. Rev. Research 5, L022052 – Published 8 June, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022052

Abstract

In multicellular systems, single-cell behaviors should be coordinated consistently with the overall population dynamics and functions. However, the interrelation between single-cell rules and the population-level goal is still elusive. In this work, we reveal that these two levels are naturally connected via a gradient flow structure of heterogeneous cellular populations and that biologically prevalent single-cell rules, such as unidirectional type switching and hierarchical order in types, emerge from this structure. We also demonstrate the gradient flow structure in a standard model of the T-cell immune response. This theoretical framework works as a basis for understanding multicellular dynamics and functions.

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References (35)

  1. F. Alenzi, B. Alenazi, M. Salem, A. Al-Jabri, and R. Wyse, The haemopoietic stem cell: Between apoptosis and self renewal, Yale J. Biol. Med. 82, 7 (2009).
  2. Y. Lee, M. Decker, H. Lee, and L. Ding, Extrinsic regulation of hematopoietic stem cells in development, homeostasis and diseases, WIREs Dev. Biol. 6, e279 (2017).
  3. G. von Dassow, E. Meir, E. M. Munro, and G. M. Odell, The segment polarity network is a robust developmental module, Nature 406, 188 (2000).
  4. D. E. Wagner, C. Weinreb, Z. M. Collins, J. A. Briggs, S. G. Megason, and A. M. Klein, Single-cell mapping of gene expression landscapes and lineage in the zebrafish embryo, Science 360, 981 (2018).
  5. H. Cheng, Z. Zheng, and T. Cheng, New paradigms on hematopoietic stem cell differentiation, Protein & Cell 11, 34 (2020).
  6. S. Mani and T. Tlusty, A topological look into the evolution of developmental programs, Biophys. J. 120, 4193 (2021).
  7. S. Ruijtenberg and S. van den Heuvel, Coordinating cell proliferation and differentiation: Antagonism between cell cycle regulators and cell type-specific gene expression, Cell Cycle 15, 196 (2016).
  8. C. Waddington, The Strategy of the Genes (George Allen & Unwin LTD, London, 1957), p. 274.
  9. S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theor. Biol. 22, 437 (1969).
  10. J. Wang, L. Xu, and E. Wang, Potential landscape and flux framework of nonequilibrium networks: Robustness, dissipation, and coherence of biochemical oscillations, Proc. Natl. Acad. Sci. USA 105, 12271 (2008).
  11. C. Furusawa and K. Kaneko, Emergence of rules in cell society: Differentiation, hierarchy, and stability, Bull. Math. Biol. 60, 659 (1998).
  12. C. Furusawa and K. Kaneko, Theory of robustness of irreversible differentiation in a stem cell system: Chaos hypothesis, J. Theor. Biol. 209, 395 (2001).
  13. C. Furusawa and K. Kaneko, A dynamical-systems view of stem cell biology, Science 338, 215 (2012).
  14. R. J. De Boer and A. S. Perelson, Quantifying T lymphocyte turnover, J. Theor. Biol. 327, 45 (2013).
  15. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L022052 for the derivation of equations, and mathematical and biological details, which includes Refs.  [30, 31, 32, 33, 34, 35].
  16. L. Ambrosio, N. Gigli, and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures (Birkhäuser, Basel, 2005), p. 334.
  17. A. Mielke, A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, Nonlinearity 24, 1329 (2011).
  18. A. Mielke, M. A. Peletier, and D. R. M. Renger, On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion, Potential Anal. 41, 1293 (2014).
  19. R. J. De Boer and A. S. Perelson, Towards a general function describing T cell proliferation, J. Theor. Biol. 175, 567 (1995).
  20. R. Antia, C. T. Bergstorm, S. S. Pilyugin, S. M. Kaech, and R. Ahmed, Models of CD8+ responses: 1. What is the antigen-independent proliferation program, J. Theor. Biol. 221, 585 (2003).
  21. A. J. Anelone and S. K. Spurgeon, Modelling and simulation of the dynamics of the antigen-specific T cell response using variable structure control theory, PLoS One 11, e0166163 (2016).
  22. R. J. De Boer, M. Oprea, R. Antia, K. Murali-Krishna, R. Ahmed, and A. S. Perelson, Recruitment times, proliferation, and apoptosis rates during the CD8+ T-cell response to lymphocytic choriomeningitis virus, J. Virol. 75, 10663 (2001).
  23. I. den Braber, T. Mugwagwa, N. Vrisekoop, L. Westera, R. Mögling, A. Bregje de Boer, N. Willems, E. Schrijver, G. Spierenburg, K. Gaiser, E. Mul, S. Otto, A. Ruiter, M. Ackermans, F. Miedema, J. Borghans, R. de Boer, and K. Tesselaar, Maintenance of peripheral naive T cells is sustained by thymus output in mice but not humans, Immunity 36, 288 (2012).
  24. T. J. Kobayashi, D. Loutchko, A. Kamimura, and Y. Sughiyama, Kinetic derivation of the Hessian geometric structure in chemical reaction networks, Phys. Rev. Res. 4, 033066 (2022).
  25. N. Ab Azar, A. Shahmansoorian, and M. Davoudi, From inverse optimal control to inverse reinforcement learning: A historical review, Annu. Rev. Control 50, 119 (2020).
  26. P. Zhou, S. Wang, T. Li, and Q. Nie, Dissecting transition cells from single-cell transcriptome data through multiscale stochastic dynamics, Nat. Commun. 12, 5609 (2021).
  27. R. C. Kraaij, A. Lazarescu, C. Maes, and M. Peletier, Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation, Stochastic Processes Appl. 130, 139 (2020).
  28. T. J. Kobayashi, D. Loutchko, A. Kamimura, and Y. Sughiyama, Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions, Phys. Rev. Res. 4, 033208 (2022).
  29. M. A. Peletier, Variational modelling: Energies, gradient flows, and large deviations, arXiv:1402.1990.
  30. J. Dolbeault, B. Nazaret, and G. Savaré, A new class of transport distances between measures, Calc. Var. Partial Differ. Equations 34, 193 (2009).
  31. M. Liero, A. Mielke, and G. Savaré, Optimal transport in competition with reaction: The Hellinger–Kantorovich distance and geodesic curves, SIAM J. Math. Anal. 48, 2869 (2016).
  32. S. Kondratyev, L. Monsaingeon, and D. Vorotnikov, A new optimal transport distance on the space of finite radon measures, Adv. Differential Equations 21, 1117 (2016).
  33. L. Chizat, G. Peyré, B. Schmitzer, and F.-X. Vialard, An interpolating distance between optimal transport and Fisher-Rao metrics, Found. Comput. Math. 18, 1 (2018).
  34. A. Esposito, F. S. Patacchini, A. Schlichting, and D. Slepčev, Nonlocal-interaction equation on graphs: Gradient flow structure and continuum limit, Arch. Ration. Mech. Anal. 240, 699 (2021).
  35. D. Homann, L. Teyton, and M. B. A. Oldstone, Differential regulation of antiviral T-cell immunity results in stable CD8+ but declining CD4+ T-cell memory, Nat. Med. 7, 913 (2001).

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Phys. Rev. Research 5, L022052– Published 8 June, 2023
  • Received 26 May 2022
  • Accepted 11 May 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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