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Spatial pattern formation in microtubule post-translational modifications and the tight localization of motor-driven cargo

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Abstract

Microtubule (MT) “age” can be interpreted as nucleotide state, lattice defects, or post-translational modification (PTM) such as acetylation and detyrosination. In all three cases, these have been recently shown to have functionally-important effects on the dynamics of MT arrays, and can present spatial and temporal heterogeneity. While mathematical models for MT array densities are well-established, here we present equations describing MT age, defined as the mean time since the MT’s building blocks (tubulin) were polymerized from their soluble dimer state. We derive the age equations using a mean first-passage time calculation and two complementary approaches: The continuum limit of spatial discretization model, and an adjoint operator approach. These equations can recapitulate the observation that the oldest (most de-tyrosinated) tubulin in axons is near the middle of axons during neuronal development in chick embryos. Furthermore, PTMs influence motor kinetics up to approximately twofold for off-rates and velocities. Our simulations demonstrate that this relatively weak dependence of motor kinetics is sufficient to target motor cargo to a specific location along the array. This localization is tightly peaked in a way that magnifies the relatively small signal of PTM spatial heterogeneity. Thus, MT age can produce long-range spatial patterning without feedbacks or diffusing signals.

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Acknowledgments

We thank Yoichiro Mori, Jay Newby and Frederic Wan for valuable discussion. This work was supported by NSF CAREER award DMS-1454739 to JA.

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Authors and Affiliations

  1. Departments of Mathematics and Physics and Astronomy, Center for Complex Biological Systems, University of California at Irvine, Irvine, CA, 92617, USA

    Jun Allard

  2. Center for Complex Biological Systems, University of California at Irvine, Irvine, CA, 92617, USA

    Abdon Iniguez & Jun Allard

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  1. Abdon Iniguez
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  2. Jun Allard
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Correspondence to Jun Allard.

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Iniguez, A., Allard, J. Spatial pattern formation in microtubule post-translational modifications and the tight localization of motor-driven cargo. J. Math. Biol. 74, 1059–1080 (2017). https://doi.org/10.1007/s00285-016-1053-x

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  • DOI: https://doi.org/10.1007/s00285-016-1053-x

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