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Crafts.jl

Crafts.jl (Combinatorial Analysis Framework for Targeted Self-assembly) computes and optimizes the equilibrium properties and assembly kinetics of mixtures of self-assembling particles.

Starting from a set of binding rules defined within its partner package Roly.jl, Crafts.jl enumerates every structure those rules allow and then predicts their number densities and yields. It further allows investigation of the assembly kinetics by integrating the rate equations governing the assembly.

Installation

using Pkg
Pkg.add(url="https://github.com/goodrichgroup/Roly.jl")
Pkg.add(url="https://github.com/goodrichgroup/Crafts.jl")

A first example

Three species of square particle that bind into a chain:

julia> using Crafts, Roly

julia> rules = BindingRules([1 1 2 3; 2 1 3 3], UnitSquare);

julia> asys = AssemblySystem(rules, EntropyModel(TreeLike(); embed3d=true))
AssemblySystem[n=3, k=2]

n is the number of species and k the number of bond types. The structures those rules allow are enumerated on first use:

julia> nstructures(asys)
6

julia> nparticles.(structures(asys))
6-element Vector{Int64}:
 1
 1
 1
 2
 2
 3

Equilibrium number densities follow from the particle concentrations and the bond energies:

julia> ϕs, εs = fill(0.1, 3), fill(8.0, 2);

julia> round.(densities(asys, ϕs, εs); digits=4)
6-element Vector{Float64}:
 0.0399
 0.0159
 0.0399
 0.024
 0.024
 0.0361

The last entry is the full three-particle chain. yields gives the same thing as fractions of all structures present, which puts the chain at 20%.

To follow the assembly in time instead, build a reaction network and integrate the rate equations:

julia> net = ReactionNetwork(asys)
ReactionNetwork[4/4 reactions active]

julia> ts, ρs = simulate_kinetics(net, ϕs, εs; T=1000.0);

julia> round.(ρs[:, end]; digits=4)
6-element Vector{Float64}:
 0.0399
 0.0159
 0.0399
 0.024
 0.024
 0.0361

ρs holds number densities, one column per time point in ts, so the last column is the equilibrium computed above.

Where to go next

  • Assembly systems — enumerating structures and their partition functions.
  • Bond potentials — modelling the interaction, and the solvers that integrate it out.
  • Equilibrium — yields, densities, and their derivatives.
  • Kinetics — reaction networks, rate kernels, and time integration.
  • Stability — relaxation modes around equilibrium.
  • Diffusion and rates — hydrodynamics and diffusion-limited binding rates.