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Dimensionality reduction in bulk-boundary reaction-diffusion systems.

Tom Burkart1, Benedikt J Müller1, Erwin Frey1,2

  • 1Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, <a href="https://ror.org/05591te55">Ludwig-Maximilians-Universität München</a>, Theresienstraße 37, D-80333 München, Germany.

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Summary
This summary is machine-generated.

This study introduces a new computational framework to accurately model intracellular protein patterns. The method efficiently analyzes protein dynamics in cells, even with changing shapes, improving our understanding of cellular functions.

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Area of Science:

  • Cellular dynamics and pattern formation
  • Computational biology and biophysics

Background:

  • Intracellular protein patterns are crucial for cellular functions like information processing and shape control.
  • Modeling protein dynamics requires coupling membrane and cytosol interactions, but standard methods struggle with dimensional differences and cytosolic gradients.

Purpose of the Study:

  • To develop a generic computational framework for projecting cytosolic protein dynamics onto a lower-dimensional surface.
  • To accurately account for cytosolic concentration gradients in static and evolving cell geometries.
  • To provide an efficient and accurate method for analyzing pattern formation with surface-volume coupling.

Main Methods:

  • Developed a framework to approximate cytosolic dynamics using a basis of characteristic concentration profiles.
  • Applied the method to a model of volume-dependent interrupted coarsening.
  • Evaluated accuracy across different basis choices for static and evolving geometries.

Main Results:

  • The proposed framework effectively projects cytosolic dynamics onto the cell surface, respecting concentration gradients.
  • The method demonstrates accuracy in analyzing pattern formation with surface-volume coupling.
  • Identified optimal basis choices for biologically relevant systems.

Conclusions:

  • This generic framework offers an efficient and accurate approach for analyzing intracellular pattern formation in complex cellular geometries.
  • The method overcomes limitations of standard numerical tools when dealing with surface-volume coupling.
  • Provides a valuable tool for studying spatiotemporal information processing and cell shape regulation.