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\( \gdef\kfh{\hat{k}_\text{f}} \gdef\kf{k_\text{f}} \gdef\ratt{r_\text{att}} \gdef\rdet{r_\text{det}} \gdef\gmc{G_\text{mc}} \gdef\gse{G_\text{se}} \gdef\conc#1{\left[#1\right]} \gdef\dgse{\Delta G^\circ_\text{se}} \)

Kinetic Tile Assembly Model (kTAM)

The kinetic Tile Assembly Model, along with the abstract Tile Assembly Model, were introduced in Winfree 19981; Evans and Winfree 2017 is a modern review on the model2.

\[ \begin{align*} \gmc &\equiv - \log \left( \conc{t} / u_0 \right) + \alpha \\ \gse &\equiv - \dgse / R T \end{align*} \]
\[ \begin{align*} \ratt &= \kf u_0 e^{-\gmc + \alpha} \\ \rdet &= \kf u_0 e^{-b \gse + \alpha} \end{align*} \]

Rgrow implements the

  • Zero-strength attachments events are ignored (equivalent to the TODO_FIND_THIS option in xgrow).
  • Fission events, which are not addressed in the kTAM definition, may be handled in several different ways (see Fission below).

Fission

Fission occurs when a detachment event would split the assembly into multiple disconnected fragments. The fission option controls how this is handled:

  • NoFission (aliases: off, no-fission):
    Any detachment event that would result in fission is prohibited. Detailed balance is preserved. This is similar to 'no' in Xgrow.

  • JustDetach (aliases: just-detach, surface):
    Allow detachment; all resulting fragments remain on the canvas, even if disconnected. Detailed balance is preserved.

  • KeepSeeded (aliases: on, keep-seeded):
    After fission, keep only fragments containing a seed tile. Remove all other fragments. Detailed balance is violated. This is similar to 'on' or 'chunk' in Xgrow, depending on the chunk settings.

  • KeepLargest (alias: keep-largest):
    After fission, keep only the largest fragment (by tile count). Remove all others. Detailed balance is violated.

  • KeepWeighted (alias: keep-weighted): After fission, randomly keep one fragment with probability proportional to its size. Remove all others. Detailed balance is violated.

  1. Winfree, E. (1998). Simulations of Computing by Self-Assembly. Caltech Technical Report CS-TR:1998.22. DOI: 10.7907/Z9TB14X7 ↩

  2. Evans, C. & Winfree, E. (2017). Physical Principles for DNA Tile Self-Assembly. Chemical Society Reviews, 46(12), 3808–3829. DOI: 10.1039/C6CS00745G ↩