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Paul M Dodd1, Pablo F Damasceno2, Sharon C Glotzer3,2,4,5

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We found that the topology of 2D molecular nets, like compactness and cutting graph leaves, predicts their folding propensity into 3D shapes. This discovery aids in designing molecules that fold into desired 3D structures.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Biophysics

Background:

  • Designing 2D molecular objects to fold into specific 3D structures is challenging.
  • Intrinsic features of low-dimensional objects influence their 3D folding propensity.

Purpose of the Study:

  • Investigate the relationship between 2D net topology and 3D folding propensity.
  • Develop a predictive method for designing self-folding molecular structures.

Main Methods:

  • Employed molecular dynamics simulations to study the refolding of 2D nets (unfoldings) of Platonic solids.
  • Analyzed net compactness and cutting graph properties to correlate with folding propensity.
  • Enumerated folding pathways and identified a crossover temperature influencing folding mechanisms.

Main Results:

  • Net compactness and cutting graph leaves correlate with thermodynamic folding propensity.
  • Identified a crossover temperature distinguishing folding via nonnative vs. native contacts.
  • Developed a numerical method to efficiently compute high-temperature folding pathways for any net.

Conclusions:

  • Net topology is a key determinant of 3D folding propensity.
  • Folding above the crossover temperature exhibits a universal balance between entropy reduction and potential energy gain.
  • The findings provide a heuristic for designing 2D objects with predictable 3D folding behavior.