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Extracting Landscape Features from Single Particle Trajectories

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Hybrid Systems Biology (HSB 2019)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 11705))

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Abstract

The predictive power of dynamical models of cell signaling is often limited due to the difficulty in estimating the relevant kinetic parameters. Super-resolution microscopy techniques can provide in vivo trajectories of individual receptors, and serve as a direct source of quantitative information on molecular processes. Single particle tracking (SPT) has been used to extract reaction kinetic parameters such as dimer lifetimes and diffusion rates. However, signaling models aim to characterize kinetics relevant to the entire cell while SPT follows individual molecules in a small fraction of the cell. The gap in resolution can be bridged with spatial simulations of molecular movement, validated at SPT resolution, which are used to infer effective kinetics on larger spatial scales.

Our focus is on processes that involve receptors bound to the cell membrane. Extrapolating kinetics observed at SPT resolution must take into account the spatial structures that interferes with the free movement of molecules of interest. This is reflected in patterns of movement that deviate from standard Brownian motion. Ideally, simulations at SPT resolution should reproduce observed movement patterns, which reflect the properties and transformation of the molecules as well as those of the underlying cell membrane.

We first sought to identify general signatures of the underlying membrane landscape in jump size distributions extracted from SPT data. We found that Brownian motion simulations in the presence of a pattern of obstacles could provide a good qualitative match. The next step is to infer the underlying landscape structures. We discuss our method used to identify such structures from long single particle trajectories that are obtained at low density. Our approach is based on deviations from ideal Brownian motion and identifies likely regions that trap receptors. We discuss the details of the method in its current form and outline a framework aimed at refinement using simulated motion in a known landscape.

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Notes

  1. 1.

    Brownian motion, as well as confinement to the cell membrane, result from interaction with much smaller molecules such as the lipids that form the membrane. We do not explicitly address this level of interaction.

  2. 2.

    not to be confused with the distribution of the magnitude of the displacement \(f(\varDelta r)\propto (\varDelta r) \exp (-(\varDelta r)/ 4 D \tau )\).

  3. 3.

    ... of comparable size, \(~10\,\mathrm {nm}\).

  4. 4.

    This implies that two points will be connected if there is a connecting path \(\{A=M_{0}, M_{1},\cdots M_{q}=B\}\) through any number of other points and no edge longer than L, \(|\varvec{r}_{M_j} - \varvec{r}_{M_{j+1}}|<L\).

  5. 5.

    This is not completely unique, but will always provide a closed polygonal line.

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Author information

Authors and Affiliations

  1. Department of Mathematics, West Virginia University, Morgantown, WV, USA

    Ádám M. Halász, Brandon L. Clark & Ouri Maler

  2. VERIMAG, Université Grenoble Alpes, Grenoble, France

    Ouri Maler

  3. N. M. Center for the SpatioTemporal Modeling of Cell Signaling, University of New Mexico, Albuquerque, NM, USA

    Jeremy S. Edwards

  4. Departments of Chemical and Biological Engineering, Chemistry and Chemical Biology, Molecular Genetics and Microbiology, University of New Mexico, Albuquerque, NM, USA

    Jeremy S. Edwards

Authors
  1. Ádám M. Halász
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  2. Brandon L. Clark
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  4. Jeremy S. Edwards
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Correspondence to Ádám M. Halász .

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Editors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Milan Češka

  2. University of London, Royal Holloway, Egham, UK

    Nicola Paoletti

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Halász, Á.M., Clark, B.L., Maler, O., Edwards, J.S. (2019). Extracting Landscape Features from Single Particle Trajectories. In: Češka, M., Paoletti, N. (eds) Hybrid Systems Biology. HSB 2019. Lecture Notes in Computer Science(), vol 11705. Springer, Cham. https://doi.org/10.1007/978-3-030-28042-0_7

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  • DOI: https://doi.org/10.1007/978-3-030-28042-0_7

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