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Optical Tweezers to Study RNA-Protein Interactions in Translation Regulation

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Shepherd model for knot-limited polymer ejection from a capsid.

Tibor Antal¹, P L Krapivsky, S Redner

¹Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA. tibor_antal@harvard.edu

Journal of Theoretical Biology

|August 26, 2009

Summary

This summary is machine-generated.

We developed a model for how knotted polymers exit spherical capsids through small pores. Ejection speed decreases with more knots, following a 1/L scaling, and is driven by internal pressure.

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Area of Science:

Polymer physics
Biophysics
Statistical mechanics

Background:

Biological macromolecules like DNA and proteins are often confined within viral capsids.
Ejection of these polymers through narrow pores is crucial for biological processes but challenging to model.
Knots in polymers can significantly impede their translocation through confined spaces.

Purpose of the Study:

To develop a tractable model for the ejection dynamics of knotted polymers from spherical capsids.
To investigate the influence of knot number on polymer ejection rates.
To establish theoretical frameworks for understanding polymer translocation through nanopores.

Main Methods:

Constructed a theoretical model based on reptation dynamics and symmetric exclusion on a line.
Incorporated internal capsid pressure as a biased particle driving knot translocation.
Computed exact ejection speeds for a finite number of knots (L).
Mapped the system to the solvable zero-range process.
Developed a continuum theory for systems with many knots.

Main Results:

The polymer ejection speed scales inversely with the number of knots (1/L).
The model provides an exact solution for finite knot numbers.
A mapping to the zero-range process simplifies analysis.
The continuum theory accurately approximates the discrete model for large L.

Conclusions:

Internal capsid pressure is a key driver for knot ejection.
Polymer knotting significantly hinders translocation, with speed inversely proportional to knot count.
The developed model and theories offer valuable insights into polymer dynamics in confined biological systems.