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Connecting Actin Polymer Dynamics Across Multiple Scales

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Using Mathematics to Understand Biological Complexity

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 22))

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Abstract

Actin is an intracellular protein that constitutes a primary component of the cellular cytoskeleton and is accordingly crucial for various cell functions. Actin assembles into semi-flexible filaments that cross-link to form higher order structures within the cytoskeleton. In turn, the actin cytoskeleton regulates cell shape, and participates in cell migration and division. A variety of theoretical models have been proposed to investigate actin dynamics across distinct scales, from the stochastic nature of protein and molecular motor dynamics to the deterministic macroscopic behavior of the cytoskeleton. Yet, the relationship between molecular-level actin processes and cellular-level actin network behavior remains understudied, where prior models do not holistically bridge the two scales together.

In this work, we focus on the dynamics of the formation of a branched actin structure as observed at the leading edge of motile eukaryotic cells. We construct a minimal agent-based model for the microscale branching actin dynamics, and a deterministic partial differential equation (PDE) model for the macroscopic network growth and bulk diffusion. The microscale model is stochastic, as its dynamics are based on molecular level effects. The effective diffusion constant and reaction rates of the deterministic model are calculated from averaged simulations of the microscale model, using the mean displacement of the network front and characteristics of the actin network density. With this method, we design concrete metrics that connect phenomenological parameters in the reaction-diffusion system to the biochemical molecular rates typically measured experimentally. A parameter sensitivity analysis in the stochastic agent-based model shows that the effective diffusion and growth constants vary with branching parameters in a complementary way to ensure that the outward speed of the network remains fixed. These results suggest that perturbations to microscale rates can have significant consequences at the macroscopic level, and these should be taken into account when proposing continuum models of actin network dynamics.

The authors “Brittany Bannish, Kelsey Gasior, Rebecca L. Pinals, and Minghao W. Rostami” contributed equally.

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Acknowledgements

The work described herein was initiated during the Collaborative Workshop for Women in Mathematical Biology hosted by the Institute for Pure and Applied Mathematics at the University of California, Los Angeles in June 2019. Funding for the workshop was provided by IPAM, the Association for Women in Mathematics’ NSF ADVANCE “Career Advancement for Women Through Research-Focused Networks” (NSF-HRD 1500481) and the Society for Industrial and Applied Mathematics. The authors thank the organizers of the IPAM-WBIO workshop (Rebecca Segal, Blerta Shtylla, and Suzanne Sindi) for facilitating this research.

R.L.P. is supported by the NSF Graduate Research Fellowships (NSF DGE 1752814). M.W.R. is supported in part by NSF DMS-1818833. A.T.D. is supported by NSF DMS-1554896.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computational Medicine Program, University of North Carolina Chapel Hill, Chapel Hill, NC, USA

    Calina Copos

  2. Department of Mathematics & Statistics, University of Central Oklahoma, Edmond, OK, USA

    Brittany Bannish

  3. Department of Mathematics, Florida State University, Tallahassee, FL, USA

    Kelsey Gasior

  4. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA, USA

    Rebecca L. Pinals

  5. Department of Mathematics and BioInspired Syracuse, Syracuse University, Syracuse, NY, USA

    Minghao W. Rostami

  6. The Ohio State University, Columbus, OH, USA

    Adriana T. Dawes

Authors
  1. Calina Copos
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  2. Brittany Bannish
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  4. Rebecca L. Pinals
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  5. Minghao W. Rostami
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  6. Adriana T. Dawes
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Correspondence to Adriana T. Dawes .

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Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, USA

    Rebecca Segal

  2. Department of Mathematics, Pomona College, Claremont, CA, USA

    Blerta Shtylla

  3. Department of Applied Mathematics, University of California, Merced, CA, USA

    Suzanne Sindi

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Copos, C., Bannish, B., Gasior, K., Pinals, R.L., Rostami, M.W., Dawes, A.T. (2021). Connecting Actin Polymer Dynamics Across Multiple Scales. In: Segal, R., Shtylla, B., Sindi, S. (eds) Using Mathematics to Understand Biological Complexity. Association for Women in Mathematics Series, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-57129-0_2

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